Answer :
Let's simplify the expression [tex]\(\sqrt[3]{5x} \cdot \sqrt[3]{25x^2}\)[/tex].
Step 1: Combine the cube roots into a single cube root.
We can express the product of two cube roots as a single cube root:
[tex]\[
\sqrt[3]{5x} \cdot \sqrt[3]{25x^2} = \sqrt[3]{(5x) \cdot (25x^2)}
\][/tex]
Step 2: Simplify inside the cube root.
Multiply the terms inside the cube root:
[tex]\[
(5x) \cdot (25x^2) = 5 \cdot 25 \cdot x \cdot x^2
\][/tex]
[tex]\[
= 125x^3
\][/tex]
Step 3: Simplify the cube root.
Find the cube root of the expression:
[tex]\[
\sqrt[3]{125x^3}
\][/tex]
- The cube root of 125 is 5 because [tex]\(5^3 = 125\)[/tex].
- The cube root of [tex]\(x^3\)[/tex] is [tex]\(x\)[/tex].
Therefore:
[tex]\[
\sqrt[3]{125x^3} = 5x
\][/tex]
Thus, the simplified expression is [tex]\(5x\)[/tex].
So, the correct answer is [tex]\(5x\)[/tex].
Step 1: Combine the cube roots into a single cube root.
We can express the product of two cube roots as a single cube root:
[tex]\[
\sqrt[3]{5x} \cdot \sqrt[3]{25x^2} = \sqrt[3]{(5x) \cdot (25x^2)}
\][/tex]
Step 2: Simplify inside the cube root.
Multiply the terms inside the cube root:
[tex]\[
(5x) \cdot (25x^2) = 5 \cdot 25 \cdot x \cdot x^2
\][/tex]
[tex]\[
= 125x^3
\][/tex]
Step 3: Simplify the cube root.
Find the cube root of the expression:
[tex]\[
\sqrt[3]{125x^3}
\][/tex]
- The cube root of 125 is 5 because [tex]\(5^3 = 125\)[/tex].
- The cube root of [tex]\(x^3\)[/tex] is [tex]\(x\)[/tex].
Therefore:
[tex]\[
\sqrt[3]{125x^3} = 5x
\][/tex]
Thus, the simplified expression is [tex]\(5x\)[/tex].
So, the correct answer is [tex]\(5x\)[/tex].
