Question

3√ -216 =.................​

Answer 1

$216 = 2 \times 108 \\ \\ 2 \times 108 = 2 \times 2 \times 54 \\ \\ 4 \times 54 = 4 \times 2 \times 27 \\ \\ 4 \times 2 \times 27 = 4 \times 2 \times 9 \times 3 \\ \\ \pink{hence} \\ \\ 216 = 4 \times 9 \times 6 \\ \\ \sqrt{216} = \sqrt{4 \times 9 \times 6} \\ \\ \sqrt{ - 216} = \sqrt{ - 4 \times 9 \times 6} \\ \\ \sqrt{ - 216} = 2 \times 3 \sqrt{ - 6} \\ \\ 3 \sqrt{ - 216} </p><p> = 3 \times 2 \times 3 \sqrt{6 {i}^{2} } \\ \\ \pink{since \: \: \: {i}^{2} = - 1} \\ \\ 3 \sqrt{ - 216} </p><p> = 18i \sqrt{6}$

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Answer 2

$3 \sqrt{ - 216} = { - 6}^{3}$