Question

express in simplified form.
\sqrt3{135}
\sqrt3{135} = \square \cdot \sqrt3{\square}

Explanation:

Step1: Factor 135 into cube factor

$135 = 27 \times 5 = 3^3 \times 5$

Step2: Split cube root using product rule

$\sqrt[3]{135} = \sqrt[3]{3^3 \times 5} = \sqrt[3]{3^3} \cdot \sqrt[3]{5}$

Step3: Simplify the perfect cube root

$\sqrt[3]{3^3} = 3$

Answer:

$\sqrt[3]{135} = 3 \cdot \sqrt[3]{5}$