Question

question 4 of 5
select the correct answer.
which of the following is equal to the expression below?
$(625 \cdot 48)^\frac{1}{4}$
60
30
$10 \sqrt{3}$
$40 \sqrt4{3}$

Explanation:

Step1: Split product under root

$\sqrt[4]{625 \cdot 48} = \sqrt[4]{625} \cdot \sqrt[4]{48}$

Step2: Simplify $\sqrt[4]{625}$

$\sqrt[4]{625} = \sqrt[4]{5^4} = 5$

Step3: Factor 48 for root simplification

$\sqrt[4]{48} = \sqrt[4]{16 \cdot 3} = \sqrt[4]{16} \cdot \sqrt[4]{3}$

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

$\sqrt[4]{16} = \sqrt[4]{2^4} = 2$

Step5: Multiply all simplified terms

$5 \cdot 2 \cdot \sqrt[4]{3} = 10\sqrt[4]{3}$

Answer:

$10\sqrt[4]{3}$ (Option 3)