Solve 5isqrt{-54}

$$5 i \sqrt { - 54 }$$

Evaluate

$$-15\sqrt{6}\approx -36.742346142$$

Solution Steps

Factor -54=\left(3i\right)^{2}\times 6. Rewrite the square root of the product \sqrt{\left(3i\right)^{2}\times 6} as the product of square roots \sqrt{\left(3i\right)^{2}}\sqrt{6}. Take the square root of \left(3i\right)^{2}.

$$5i\times \left(3i\right)\sqrt{6}$$

Multiply 5i and 3i to get -15.

$$-15\sqrt{6}$$

Real Part

$$-15\sqrt{6}$$