square root


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square root - a factor of a number that, when multiplied by itself, gives the original number
Formula: √x

1/3c increased by the square root of d
1/3c increased by the square root of d square root of d: sqrt(d) 1/3c increased by the square root of d [B]1/3c + sqrt(d)[/B]

1/n^2 = 3/192
1/n^2 = 3/192 Cross multiply: 192 * 1 = 3 * n^2 3n^2 = 192 Divide each side by 3: 3n^2/3 = 192/3 Cancel the 3's on the left side: n^2 = 64 Take the square root of both sides: n = [B]8 or -8[/B]

A bird was sitting 12 meters from the base of an oak tree and flew 15 meters to reach the top of the
A bird was sitting 12 meters from the base of an oak tree and flew 15 meters to reach the top of the tree. How tall is the tree? So we have a [U]right triangle[/U]. Hypotenuse is 15. Base is 12. We want the length of the leg. The formula for a right triangle relation of sides is a^2 + b^2 = c^2 where c is the hypotenuse and a, b are the sides Rearranging this equation to isolate a, we get a^2 = c^2 - b^2 Taking the square root of both sides, we get a = sqrt(c^2 - b^2) a = sqrt(15^2 - 12^2) a = sqrt(225 - 144) a = sqrt(81) a = [B]9 meters[/B]

Approximate Square Root Using Exponential Identity
Free Approximate Square Root Using Exponential Identity Calculator - Calculates the square root of a positive integer using the Exponential Identity Method

a^2 + b62 = c^2 for c
a^2 + b^2 = c^2 for c Take the square root of each side: c = [B]sqrt(a^2 + b^2)[/B]

Babylonian Method
Free Babylonian Method Calculator - Determines the square root of a number using the Babylonian Method.

Bakshali Method
Free Bakshali Method Calculator - Calculates the square root of a positive integer using the Bakshali Method

Basic Statistics
Free Basic Statistics Calculator - Given a number set, and an optional probability set, this calculates the following statistical items:
Expected Value
Mean = μ
Variance = σ2
Standard Deviation = σ
Standard Error of the Mean
Skewness
Mid-Range
Average Deviation (Mean Absolute Deviation)
Median
Mode
Range
Pearsons Skewness Coefficients
Entropy
Upper Quartile (hinge) (75th Percentile)
Lower Quartile (hinge) (25th Percentile)
InnerQuartile Range
Inner Fences (Lower Inner Fence and Upper Inner Fence)
Outer Fences (Lower Outer Fence and Upper Outer Fence)
Suspect Outliers
Highly Suspect Outliers
Stem and Leaf Plot
Ranked Data Set
Central Tendency Items such as Harmonic Mean and Geometric Mean and Mid-Range
Root Mean Square
Weighted Average (Weighted Mean)
Frequency Distribution
Successive Ratio

Complex Number Operations
Free Complex Number Operations Calculator - Given two numbers in complex number notation, this calculator:
1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.
2) Determines the Square Root of a complex number denoted as √a + bi
3) Absolute Value of a Complex Number |a + bi|
4) Conjugate of a complex number a + bi

difference between 2 positive numbers is 3 and the sum of their squares is 117
difference between 2 positive numbers is 3 and the sum of their squares is 117 Declare variables for each of the two numbers: [LIST] [*]Let the first variable be x [*]Let the second variable be y [/LIST] We're given 2 equations: [LIST=1] [*]x - y = 3 [*]x^2 + y^2 = 117 [/LIST] Rewrite equation (1) in terms of x by adding y to each side: [LIST=1] [*]x = y + 3 [*]x^2 + y^2 = 117 [/LIST] Substitute equation (1) into equation (2) for x: (y + 3)^2 + y^2 = 117 Evaluate and simplify: y^2 + 3y + 3y + 9 + y^2 = 117 Combine like terms: 2y^2 + 6y + 9 = 117 Subtract 117 from each side: 2y^2 + 6y + 9 - 117 = 117 - 117 2y^2 + 6y - 108 = 0 This is a quadratic equation: Solve the quadratic equation 2y2+6y-108 = 0 With the standard form of ax2 + bx + c, we have our a, b, and c values: a = 2, b = 6, c = -108 Solve the quadratic equation 2y^2 + 6y - 108 = 0 The quadratic formula is denoted below: y = -b sqrt(b^2 - 4ac)/2a [U]Step 1 - calculate negative b:[/U] -b = -(6) -b = -6 [U]Step 2 - calculate the discriminant ?:[/U] ? = b2 - 4ac: ? = 62 - 4 x 2 x -108 ? = 36 - -864 ? = 900 <--- Discriminant Since ? is greater than zero, we can expect two real and unequal roots. [U]Step 3 - take the square root of the discriminant ?:[/U] ?? = ?(900) ?? = 30 [U]Step 4 - find numerator 1 which is -b + the square root of the Discriminant:[/U] Numerator 1 = -b + ?? Numerator 1 = -6 + 30 Numerator 1 = 24 [U]Step 5 - find numerator 2 which is -b - the square root of the Discriminant:[/U] Numerator 2 = -b - ?? Numerator 2 = -6 - 30 Numerator 2 = -36 [U]Step 6 - calculate your denominator which is 2a:[/U] Denominator = 2 * a Denominator = 2 * 2 Denominator = 4 [U]Step 7 - you have everything you need to solve. Find solutions:[/U] Solution 1 = Numerator 1/Denominator Solution 1 = 24/4 Solution 1 = 6 Solution 2 = Numerator 2/Denominator Solution 2 = -36/4 Solution 2 = -9 [U]As a solution set, our answers would be:[/U] (Solution 1, Solution 2) = (6, -9) Since one of the solutions is not positive and the problem asks for 2 positive number, this problem has no solution

Equation and Inequalities
Free Equation and Inequalities Calculator - Solves an equation or inequality with 1 unknown variable and no exponents as well as certain absolute value equations and inequalities such as |x|=c and |ax| = c where a and c are constants. Solves square root, cube root, and other root equations in the form ax^2=c, ax^2 + b = c. Also solves radical equations in the form asqrt(bx) = c. Also solves open sentences and it will solve one step problems and two step equations. 2 step equations and one step equations and multi step equations

Estimate Square Roots
Free Estimate Square Roots Calculator - Estimates the square root of a number

Explain the relationship between "squaring" a number and finding the "square root" of a number. Use
Explain the relationship between "squaring" a number and finding the "square root" of a number. Use an example to further explain your answer. Squaring a number means raising it to the power of 2 The square root of a number [I]undoes[/I] a square of a number. So square root of x^2 is x x squared is x^2 Let x = 5. x squared = 5^2 = 25 Square root of 25 = square root of 5^2 = 5

Factoring and Root Finding
Free Factoring and Root Finding Calculator - This calculator factors a binomial including all 26 variables (a-z) using the following factoring principles:
* Difference of Squares
* Sum of Cubes
* Difference of Cubes
* Binomial Expansions
* Quadratics
* Factor by Grouping
* Common Term
This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots
* Factors and simplifies Rational Expressions of one fraction
* Determines the number of potential positive and negative roots using Descarte’s Rule of Signs

Find Mean 106 and standard deviation 10 of the sample mean which is 25
Do you mean x bar? mean of 106 inches and a standard deviation of 10 inches and for sample of size is 25. Determine the mean and the standard deviation of /x If so, x bar equals the population mean. So it's [B]106[/B]. Sample standard deviation = Population standard deviation / square root of n 10/Sqrt(25) 10/5 [B]2[/B]

find the two square roots of 81
find the two square roots of 81 When we multiply 9 * 9, we get 81 When we multiply -9 * -9, we get 81 So our two square roots of 81 are: [LIST] [*][B]-9, 9[/B] [/LIST]

Hari planted 324 plants in such a way that there were as many rows of plants as there were number of
Hari planted 324 plants in such a way that there were as many rows of plants as there were number of columns. Find the number of rows and columns. Let r be the number of rows and c be the number of columns. We have the area: rc = 324 Since rows equal columns, we have a square, and we can set r = c. c^2 = 324 Take the square root of each side: [B]c = 18[/B] Which means [B]r = 18[/B] as well. What we have is a garden of 18 x 18.

if i = square root of -1 what is the sum (7 + 3i) + (-8 + 9i)
if i = square root of -1 what is the sum (7 + 3i) + (-8 + 9i) We group like terms, and we get: 7 - 8 + (3 + 9)i Simplifying, we get: [B]-1 + 12i[/B]

Juan runs out of gas in a city. He walks 30yards west and then 16 yards south looking for a gas stat
Juan runs out of gas in a city. He walks 30yards west and then 16 yards south looking for a gas station. How far is he from his starting point? Juan is located on a right triangle. We calculate the hypotenuse: 30^2 + 16^2 = Hypotenuse^2 900 + 256 = Hypotenuse^2 Hypotenuse^2 = 1156 Take the square root of each side: [B]Hypotenuse = 34 yards[/B]

K varies inversely with square root of m and directly with the cube of n.
K varies inversely with square root of m and directly with the cube of n. [LIST] [*]We take a constant c as our constant of proportionality. [*]The word inversely means we divide [*]The word directly means we multiply [/LIST] [B]k = cn^3/sqrt(m)[/B]

Kamille is calculating the length of diagonal on a picture board and gets a solution of the square r
Kamille is calculating the length of diagonal on a picture board and gets a solution of the square root of 58. She needs to buy the ribbon to put across the diagonal of the board, so she estimates that she will need at least 60 inches of ribbon to cover the diagonal. Is she correct? Explain. [URL='https://www.mathcelebrity.com/powersq.php?num=sqrt%2858%29&pl=Calculate']The square root of 58 [/URL]has an answer between 7 and 8. So Kamille is [B]incorrect[/B]. She needs much less than 60 inches of ribbon. She needs less than 8 inches of ribbon.

Newton Method
Free Newton Method Calculator - Calculates the square root of a positive integer using the Newton Method

n^2 + 9 = 34
n^2 + 9 = 34 Subtract 9 from each side: n^2 + 9 - 9 = 34 - 9 n^2 = 25 Take the square root of each side: n = [B]5[/B]

n^2 - 1 = -99/100
n^2 - 1 = -99/100 Add 1 (100/100) to each side: n^2 - 1 + 1 = -99/100 + 100/100 Cancel the 1's on the left side: n^2 = 1/100 Take the square root of both sides: n = [B]1/10 or -1/10[/B]

n^2 = 1/4
n^2 = 1/4 Take the square root of each side: n = [B]1/2[/B]

n^2 = 6&1/4
n^2 = 6&1/4 [URL='https://www.mathcelebrity.com/fraction.php?frac1=6%261%2F4&frac2=3%2F8&pl=Simplify']6&1/4[/URL] = 25/4 n^2 = 25/4 Take the square root of each side: n = [B]5/2 or -5/2[/B]

n^2 = 64
n^2 = 64 Take the square root of each side: sqrt(n^2) = sqt(64) n = [B]8[/B]

Quadratic Equations and Inequalities
Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax2 + bx + c = 0. Also generates practice problems as well as hints for each problem.
* Solve using the quadratic formula and the discriminant Δ
* Complete the Square for the Quadratic
* Factor the Quadratic
* Y-Intercept
* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)2 + k
* Concavity of the parabola formed by the quadratic
* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.

r varies directly with s and inversely with the square root of t
r varies directly with s and inversely with the square root of t Varies directly means we multiply Varies inversely means we divide There exists a constant k such that: [B]r = ks/sqrt(t)[/B]

Rational,Irrational,Natural,Integer Property
Free Rational,Irrational,Natural,Integer Property Calculator - This calculator takes a number, decimal, or square root, and checks to see if it has any of the following properties:
* Integer Numbers
* Natural Numbers
* Rational Numbers
* Irrational Numbers Handles questions like: Irrational or rational numbers Rational or irrational numbers rational and irrational numbers Rational number test Irrational number test Integer Test Natural Number Test

rs+h^2=1 for h
rs+h^2=1 for h Subtract rs from each side to isolate h: rs - rs + h^2 = 1 - rs Cancel the rs on the left side: h^2 = 1 - rs Take the square root of each side: sqrt(h^2) = sqrt(1 - rs) [B]h = +- sqrt(1 -rs)[/B]

s = tu^2 for u
s = tu^2 for u Divide each side by t u^2 = s/t Take the square root of each side [LIST] [*]u = sqrt(s/t) [*]u = -sqrt(s/t) [/LIST] We have two answers due to negative number squared is positive

Six is the principal square root of 36
Six is the principal square root of 36 The two square roots of 36 are: [LIST] [*]+6 [*]-6 [/LIST] The positive square root is known as the principal square root, therefore, this is [B]true[/B].

Solve for h. rs + h^2 = l
Solve for h. rs + h^2 = l [U]Subtract rs from each side to isolate h:[/U] rs - rs + h^2 = l - rs [U]Cancel the rs terms on the left side, and we get:[/U] h^2 = l - rs [U]Take the square root of each side:[/U] h = [B]sqrt(l - rs)[/B]

Solve mgh=1/2mv^2+1/2(2/5)mr^2(v^2/r^2) for v
Solve mgh=1/2mv^2+1/2(2/5)mr^2(v^2/r^2) for v 1/2(2/5) = 1/5 since the 2's cancel r^2/r^2 = 1 So we simplify, and get: mgh=1/2mv^2+1/5(mv^2) for v Divide each side by m, so m's cancel in each term on the left and right side: gh = 1/2v^2 + 1/5(v^2) Combine like terms for v^2 on the right side: 1/2 + 1/5 = 7/10 from our [URL='https://www.mathcelebrity.com/fraction.php?frac1=1%2F2&frac2=1%2F5&pl=Add']fraction calculator[/URL] So we have: gh = 7v^2/10 Multiply each side by 10: 10gh = 7v^2 Now divide each side by 7 10gh/7 = v^2 Take the square root of each side: [B]v = sqrt(10gh/7)[/B]

Square root of 9136 divided by 43
Square root of 9136 divided by 43 First, [URL='https://www.mathcelebrity.com/powersq.php?num=sqrt%289136%29&pl=Calculate']take the square root of 9136 in our calculator[/URL]: 4 * sqrt(571) Now divide this by 43: [B]4 * sqrt(571) / 43[/B]

square root of the sum of 2 variables
square root of the sum of 2 variables The phrase [I]2 variables[/I] means we choose 2 arbitrary variables, let's call them x and y: x, y The sum of 2 variables means we add: x + y Square root of the sum of 2 variables is written as: [B]sqrt(x + y)[/B]

square root of x times the square root of y
square root of x times the square root of y square root of x: sqrt(x) square root of y: sqrt(y) square root of x times the square root of y [B]sqrt(x) * sqrt(y)[/B]

Square Root Table
Free Square Root Table Calculator - Generates a square root table for the first (n) numbers rounded to (r) digits

Square Roots and Exponents
Free Square Roots and Exponents Calculator - Given a number (n), or a fraction (n/m), and/or an exponent (x), or product of up to 5 radicals, this determines the following:
* The square root of n denoted as √n
* The square root of the fraction n/m denoted as √n/m
* n raised to the xth power denoted as nx (Write without exponents)
* n raised to the xth power raised to the yth power denoted as (nx)y (Write without exponents)
* Product of up to 5 square roots: √abcde
* Write a numeric expression such as 8x8x8x8x8 in exponential form

The coefficient of determination is found by taking the square root of the coefficient of correlatio
The coefficient of determination is found by taking the square root of the coefficient of correlation. True or False [B]FALSE[/B] - It is found by squaring the coefficient of correlation

The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. a) What i
The IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. a) What is the probability that a randomly person has an IQ between 85 and 115? b) Find the 90th percentile of the IQ distribution c) If a random sample of 100 people is selected, what is the standard deviation of the sample mean? a) [B]68%[/B] from the [URL='http://www.mathcelebrity.com/probnormdist.php?xone=50&mean=100&stdev=15&n=1&pl=Empirical+Rule']empirical rule calculator[/URL] b) P(z) = 0.90. so z = 1.28152 using Excel NORMSINV(0.9)
(X - 100)/10 = 1.21852 X = [B]113[/B] rounded up c) Sample standard deviation is the population standard deviation divided by the square root of the sample size 15/sqrt(100) = 15/10 =[B] 1.5[/B]

The product of a number and its square is less than 8
Let the number be x. Let the square be x^2. So we have (x)(x^2) = x^3 < 8 Take the cube root of this, we get x = 2

twice a number subtracted from the square root of the same number
twice a number subtracted from the square root of the same number The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x Twice a number means we multiply x by 2: 2x Square root of the same number: sqrt(x) twice a number subtracted from the square root of the same number [B]sqrt(x) - 2x[/B]

twice the square root of a number increased by 5 is 23
twice the square root of a number increased by 5 is 23 The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x The square root of a number means we raise x to the 1/2 power: sqrt(x) the square root of a number increased by 5 means we add 5 to sqrt(x): sqrt(x) + 5 twice the square root of a number increased by 5 means we multiply sqrt(x) + 5 by 2: 2(sqrt(x) + 5) The phrase [I]is 23[/I] means we set 2(sqrt(x) + 5) equal to 23: [B]2(sqrt(x) + 5) = 23[/B]

Use k as the constant of variation. L varies jointly as u and the square root of v.
Use k as the constant of variation. L varies jointly as u and the square root of v. Since u and v vary jointly, we multiply by the constant of variation k: [B]l = ku * sqrt(v)[/B]

Variation Equations
Free Variation Equations Calculator - This calculator solves the following direct variation equations and inverse variation equations below:
* y varies directly as x
* y varies inversely as x
* y varies directly as the square of x
* y varies directly as the cube of x
* y varies directly as the square root of x
* y varies inversely as the square of x
* y varies inversely as the cube of x
* y varies inversely as the square root of x

vw^2+y=x for w
vw^2+y=x for w This is an algebraic expression. Subtract y from each side: vw^2 + y - y = x - y The y's cancel on the left side, so we're left with: vw^2 = x - y Divide each side by v w^2 = (x - y)/v Take the square root of each side: w = [B]Sqrt((x - y)/v)[/B]

You and your friend are playing a number-guessing game. You ask your friend to think of a positive n
You and your friend are playing a number-guessing game. You ask your friend to think of a positive number, square the number, multiply the result by 2, and then add three. If your friend's final answer is 53, what was the original number chosen? Let n be our original number. Square the number means we raise n to the power of 2: n^2 Multiply the result by 2: 2n^2 And then add three: 2n^2 + 3 If the friend's final answer is 53, this means we set 2n^2 + 3 equal to 53: 2n^2 + 3 = 53 To solve for n, we subtract 3 from each side, to isolate the n term: 2n^2 + 3 - 3 = 53 - 3 Cancel the 3's on the left side, and we get: 2n^2 = 50 Divide each side of the equation by 2: 2n^2/2 = 50/2 Cancel the 2's, we get: n^2 = 25 Take the square root of 25 n = +-sqrt(25) n = +-5 We are told the number is positive, so we discard the negative square root and get: n = [B]5[/B]