Mathematics, 13.10.2020 02:01, JAlvelo

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

Answers: 2

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Answers

answered: andile64

[See Below]

Step-by-step explanation:

$\boxed{Hey~There!}$

__________________________________________________________

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

1.) $\sqrt{72}$ :

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

$\boxed{The~answer~is: 6\sqrt{2}}$

2.) $\sqrt{20}$ :

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

$\boxed{The~answer~is: 2\sqrt{5}}$

3.) $\sqrt{42}$ :

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 .

$\boxed{The~answer~is: \sqrt{42} }$

4.) $2\sqrt{12}$ :

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

$\boxed{The~answer~is: 4\sqrt{3} }$

5.) $3\sqrt{75}$ :

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

$\boxed{The~answer~is: 15\sqrt{3}}$

6.) $-2\sqrt{18}$ :

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

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

__________________________________________________________

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

answered: Guest

step-by-step explanation:

answered: Guest

The answer is the first one

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