how to find the square root of -72 using imaginary number i

Question

How do i find the square root of -72 by using the imaginary number i.

Answer 1

Think of -72 as 72i² so √(-72) = √[(2(36)(i²)] = 6i√2.

That is, we take the square roots of 2, and 36, and i², giving us the factors listed at the end of the line above--arranged to obviatae confusion, i.e. the only radical is placed at the end, and 6 & i are treated as coefficients at the beginning.