Question

simplify the expression.
select
ot a real number\ if applicable.
\sqrt3{-\frac{27}{64}} = \square

Explanation:

Step1: Split cube root of negative fraction

$\sqrt[3]{-\frac{27}{64}} = -\sqrt[3]{\frac{27}{64}}$

Step2: Split root into numerator/denominator

$-\frac{\sqrt[3]{27}}{\sqrt[3]{64}}$

Step3: Compute cube roots

$\sqrt[3]{27}=3$, $\sqrt[3]{64}=4$

Step4: Substitute values

$-\frac{3}{4}$

Answer:

$-\frac{3}{4}$