Enter square root or exponent statement:


  

Evaluate the following

2√28+3√63-√49

Term 1 has a square root, so we evaluate and simplify:

Simplify 2√28.

Checking square roots, we see that

52 = 25 and 62 = 36

Our answer in decimal format is between 5 and 6

Our answer is not an integer

Simplify it into the product of an integer and a radical.

We do this by listing each product combo of 28

Check for integer square root values below:

28 = √128

28 = √214

28 = √47

From that list, the highest factor with an integer square root is 4

Therefore, we use the product combo √28 = √47

Evaluating square roots, we see that √4 = 2

Simplifying our product of radicals, we get our answer:

Multiply by our constant of 2

2√28 = (2 x 2)√7

Term 2 has a square root, so we evaluate and simplify:

Simplify 3√63.

Checking square roots, we see that

72 = 49 and 82 = 64

Our answer in decimal format is between 7 and 8

Our answer is not an integer

Simplify it into the product of an integer and a radical.

We do this by listing each product combo of 63

Check for integer square root values below:

63 = √163

63 = √321

63 = √79

From that list, the highest factor with an integer square root is 9

Therefore, we use the product combo √63 = √97

Evaluating square roots, we see that √9 = 3

Simplifying our product of radicals, we get our answer:

Multiply by our constant of 3

3√63 = (3 x 3)√7

Term 3 has a square root, so we evaluate and simplify:

Simplify -1√49.

If you use a guess and check method, you see that 62 = 36 and 82 = 64.
Since 36 < 49 < 64 the next logical step would be checking 72.

72 = 7 x 7
72 = 49 <--- We match our original number!!!
Multiplying by our outside constant, we get -1 x 7 = -7
Therefore, -1√49 = ±-7

The principal root is the positive square root, so we have a principal root of -7

Group constants

-7 = -7

Group square root terms for 13

(4 + 9)√7

13√7


Final Answer:

-7 + 13√7


You have 2 free calculationss remaining




How does the Square Roots and Exponents Calculator work?
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
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What 3 formulas are used for the Square Roots and Exponents Calculator?

√n2 = ±n



For more math formulas, check out our Formula Dossier

What 5 concepts are covered in the Square Roots and Exponents Calculator?

exponent
The power to raise a number
fraction
how many parts of a certain size exist
a/b where a is the numerator and b is the denominator
power
how many times to use the number in a multiplication
square root
a factor of a number that, when multiplied by itself, gives the original number
√x
square roots and exponents
Example calculations for the Square Roots and Exponents Calculator

Square Roots and Exponents Calculator Video


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