Enter Equation or Inequality
  

Solve the following equation

2w^2=360

Solve for w:

2w2 = 360

Divide each side of the equation by 2

2w2
2
=
  
360
2

w2  =  360
  2

w  =  √360
  √2

Using our radical expression calculator, we can simplify this

w2 = 180

Take the square root of each side:

√w2= √180

w= = ±√180

Simplify √180

Checking square roots, we see that 132 = 169 and 142 = 196

Our answer is not an integer, so we try simplify it into the product of an integer and a radical.

We do this by listing each product combo of 180 checking for integer square root values below:

√180 = √1√180

√180 = √2√90

√180 = √3√60

√180 = √4√45

√180 = √5√36

√180 = √6√30

√180 = √9√20

√180 = √10√18

√180 = √12√15

Find the highest integer square root

The highest factor that has an integer square root is 36

Therefore, we use the product combo √180 = √36√5

Evaluating square roots, we see that √36 = 6

Final Answer

w = ±6√5


You have 2 free calculationss remaining



What is the Answer?
w = ±6√5
How does the Equation and Inequalities Calculator work?
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
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What 3 formulas are used for the Equation and Inequalities Calculator?

One Step Equations (Division): cx = b x = b/c
One Step Equations (Addition): x + c = b x = b - c
One Step Equations (Subtraction): x - c = b x = b + c

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What 4 concepts are covered in the Equation and Inequalities Calculator?

equation
a statement declaring two mathematical expressions are equal
equation and inequalities
unknown
a number or value we do not know
variable
Alphabetic character representing a number
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