Simplify each radical And show your work √72 √20 √42 2√12 3√75 -2√18

Simplify each radical And show your work √72 √20 √42 2√12 3√75 -2√18

asked Sep 6, 2021 79.0k views

1 Answer

Answer:

[See Below]

Explanation:

$\boxed{Hey~There!}$

__________________________________________________________

$\boxed{Simplify~each~radical:}$

1.)
√(72) :

Factor
into its prime factors :

72 = 23 * 32

To simplify a square root, we extract factors which are squares, factors that are raised to an even exponent.

Factors which will be extracted are:

36 = 22 * 32

Factors which will remain inside the root are:

2 = 2

To complete the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by
:

6 = 2 * 3

$\boxed{The~answer~is: 6√(2)}$

2.)
√(20) :

Factor
into its prime factors :

20 = 22 * 5

To simplify a square root, we extract factors which are squares, factors that are raised to an even exponent.

Factors which will be extracted are:

4 = 22

Factors which will remain inside the root are:

5 = 5

To complete the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by
:

2 = 2

$\boxed{The~answer~is: 2√(5)}$

3.)
√(42) :

Factor
into its prime factors :

42 = 2 * 3 * 7

To simplify a square root, we extract factors which are squares, factors that are raised to an even exponent.

In our case however, all the factors are only raised to the first power and this means that the square root can not be simplified .

$\boxed{The~answer~is: √(42) }$

4.)
2√(12) :

Factor
into its prime factors :

12 = 22 * 3

To simplify a square root, we extract factors which are squares, factors that are raised to an even exponent.

Factors which will be extracted are:

4 = 22

Factors which will remain inside the root are:

3 = 3

To complete the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by
:

2 = 2

$\boxed{The~answer~is: 4√(3) }$

5.)
3√(75) :

Factor
into its prime factors :

75 = 3 * 52

To simplify a square root, we extract factors which are squares, factors that are raised to an even exponent.

Factors which will be extracted are:

25 = 52

Factors which will remain inside the root are:

3 = 3

To complete the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by
:

5 = 5

$\boxed{The~answer~is: 15√(3)}$

6.)
-2√(18) :

Factor
into its prime factors :

18 = 2 * 32

To simplify a square root, we extract factors which are squares, factors that are raised to an even exponent.

Factors which will be extracted are:

9 = 32

Factors which will remain inside the root are:

2 = 2

To complete the simplification we take the square root of the factors which are to be extracted. We do this by dividing their exponents by
:

3 = 3

$\boxed{The~answer~is: 3√(5)~or~-6√(2)}$

__________________________________________________________

$Hope~this~helps~Mate~\\-Your~Friendly~Answerer,~Shane$ ^-^

Sardo answered Sep 11, 2021

by Sardo

8.3k points

← Prev Question Next Question →

Search Qamnty