Question

use the properties of radicals to simplify the expression. $sqrt4{6} cdot sqrt4{8} = square$

Explanation:

Step1: Multiply radicands (same index)

$\sqrt[4]{6} \cdot \sqrt[4]{8} = \sqrt[4]{6 \times 8}$

Step2: Calculate product inside radical

$\sqrt[4]{48}$

Step3: Factor out 4th power term

$\sqrt[4]{16 \times 3} = \sqrt[4]{16} \cdot \sqrt[4]{3}$

Step4: Simplify $\sqrt[4]{16}$

$\sqrt[4]{2^4} = 2$, so $2\sqrt[4]{3}$

Answer:

$2\sqrt[4]{3}$