 # 2sqrt(28)+3sqrt(63)-sqrt(49)

## Enter square root or exponent statement:

Evaluate 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, so we try simplify it into the product of an integer and a radical.

We do this by listing each product combo of 28 checking for integer square root values below:
28 = √128
28 = √214
28 = √47

From that list, the highest factor that has an integer square root is 4.
Therefore, we use the product combo √28 = √47
Evaluating square roots, we see that √4 = 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 72 = 49 and 82 = 64.
Our answer in decimal format is between 7 and 8
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 63 checking for integer square root values below:
63 = √163
63 = √321
63 = √79

From that list, the highest factor that has an integer square root is 9.
Therefore, we use the product combo √63 = √97
Evaluating square roots, we see that √9 = 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 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

-7 = -7

## Group square root terms for 13

(4 + 9)√7
13√7

-7 + 13√7

### How does the Square Roots and Exponents Calculator work?

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
This calculator has 1 input.

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

1. √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