Question

1. simplify the expression below.

$2\sqrt4{8w^3} \cdot 3\sqrt4{32w^5}$
a. $24w^2$
b. $96w^2$
c. $24w^3\sqrt4{w^3}$
d. $96w^3\sqrt4{w^3}$

Explanation:

Step1: Multiply coefficients outside roots

$2 \times 3 = 6$

Step2: Combine radicals using product rule

$\sqrt[4]{8w^3} \times \sqrt[4]{32w^5} = \sqrt[4]{8w^3 \times 32w^5}$

Step3: Simplify product inside radical

$\sqrt[4]{(8 \times 32) \times (w^3 \times w^5)} = \sqrt[4]{256w^8}$

Step4: Simplify the 4th root

$\sqrt[4]{256w^8} = \sqrt[4]{4^4 \times (w^2)^4} = 4w^2$

Step5: Multiply results from Step1 & Step4

$6 \times 4w^2 = 24w^2$

Answer:

A. $24w^2$