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

Simplify 2√28.

Checking square roots, we see that

5^{2} = 25 and 6^{2} = 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 = √1√28

√28 = √2√14

√28 = √4√7

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

Therefore, we use the product combo √28 = √4√7

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

2√28 = 4√7

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

Simplify 3√63.

Checking square roots, we see that

7^{2} = 49 and 8^{2} = 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 = √1√63

√63 = √3√21

√63 = √7√9

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

Therefore, we use the product combo √63 = √9√7

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

3√63 = 9√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 6^{2} = 36 and 8^{2} = 64. Since 36 < 49 < 64 the next logical step would be checking 7^{2}.

7^{2} = 7 x 7 7^{2} = 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

Build final answer:

-7 + 13√7

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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 x^{th} power denoted as n^{x} (Write without exponents)
* n raised to the x^{th} power raised to the yth power denoted as (n^{x})^{y} (Write without exponents)
* Product of up to 5 square roots: √a√b√c√d√e
* Write a numeric expression such as 8x8x8x8x8 in exponential form This calculator has 1 input.

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