# Simplify sqrt-54 using the imaginary number i A) 3isqrt6 B) -3sqrt6 C) isqrt54 D) 3sqrt-6

Question
Simplify sqrt-54 using the imaginary number i
A) $$\displaystyle{3}{i}\sqrt{{6}}$$
B) $$\displaystyle-{3}\sqrt{{6}}$$
C) $$\displaystyle{i}\sqrt{{54}}$$
D) $$\displaystyle{3}\sqrt{-}{6}$$

2021-01-09
For a>0, $$\displaystyle√-{a}={i}√{a}$$. Hence, $$\displaystyle√-{54}={i}√{54}={i}√{9}\cdot{6}={i}√{9}\cdot√{6}={i}{\left({3}\right)}\cdot√{6}={3}{i}√{6}$$
So, the answer is choice A.

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