Question

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

Answer 1

[See Below]

Explanation:

`\boxed{Hey~There!}`

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

1.)
`√(72)`:

• Factor
  `72` 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
  `2`:

`6 = 2 * 3`

`\boxed{The~answer~is: 6√(2)}`

2.)
`√(20)`:

• Factor
  `20` 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 = 2`

`\boxed{The~answer~is: 2√(5)}`

3.)
`√(42)`:

• Factor
  `42` 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
  `12` 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 = 2`

`\boxed{The~answer~is: 4√(3) }`

5.)
`3√(75)`:

• Factor
  `75` 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
  `2`:

`5 = 5`

`\boxed{The~answer~is: 15√(3)}`

6.)
`-2√(18)`:

• Factor
  `18` 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
  `2`:

`3 = 3`

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

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