Question

Worth 25 points!

Simplify these equations with steps please.
√-48
√-63
√-72
√-24
√-84
√-99

Answer 1

1)
`√(-48)=4√(3) \ i`

2)
`√(-63)=3√(7) \ i`

3)
`√(-72)=6√(2) \ i`

4)
`√(-24)=4√(6) \ i`

5)
`√(-84)=2√(21) \ i`

6)
`√(-99)=3√(11) \ i`

Explanation:

We need to simply the following :

Note: For all questions given we know that
`√(-1)=i` using it in all the given questions.

1)
`√(-48)`

Factors of 48 are: 2x2x2x2x3

`√(-48)\\=√(48)√(-1) \\=√(2*2*2*2*3)\ i\\= √(2^2*2^2*3)\ i\\=2*2√(3) \ i \\=4√(3) \ i`

2)
`√(-63)`

Factors of 63 are: 3x3x7

`√(-63)\\=√(63)√(-1) \\=√(3*3*7)\ i\\= √(3^2*7)\ i\\=3√(7) \ i`

3)
`√(-72)`

Factors of 72 are: 2x2x2x3x3

`√(-72)\\=√(72)√(-1) \\=√(2*2*2*3*3)\ i\\= √(2^2*3^2*2)\ i\\=2*3√(2) \ i \\=6√(2) \ i`

4)
`√(-24)`

Factors of 24 are: 2x2x2x3

`√(-24)\\=√(24)√(-1) \\=√(2*2*2*3)\ i\\= √(2^2*2*3)\ i\\=2√(2*3) \ i \\=2√(6) \ i`

5)
`√(-84)`

Factors of 84 are: 2x2x3x7

`√(-84)\\=√(84)√(-1) \\=√(2*2*3*7)\ i\\= √(2^2*3*7)\ i\\=2√(21) \ i`

6)
`√(-99)\\`

Prime factors of 99 are: 3x3x11

`√(-99)\\=√(99)√(-1) \\=√(3*3*11)\ i\\= √(3^2*11)\ i\\=3√(11) \ i \\=3√(11) \ i`