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Simplify [tex]\sqrt[3]{5x} \cdot \sqrt[3]{25x^2}[/tex] completely.

A. [tex]25x^3[/tex]
B. [tex]25x[/tex]
C. [tex]5x^3[/tex]
D. [tex]5x[/tex]

Answer :

To simplify the expression [tex]\(\sqrt[3]{5x} \cdot \sqrt[3]{25x^2}\)[/tex], we can use the property of cube roots which states:

[tex]\[
\sqrt[3]{a} \cdot \sqrt[3]{b} = \sqrt[3]{a \cdot b}
\][/tex]

Applying this property, we have:

[tex]\[
\sqrt[3]{5x} \cdot \sqrt[3]{25x^2} = \sqrt[3]{(5x) \cdot (25x^2)}
\][/tex]

Now, let's multiply the expressions inside the cube root:

[tex]\[
(5x) \cdot (25x^2) = 5 \cdot 25 \cdot x \cdot x^2
\][/tex]

Calculating the coefficients and powers, we get:

[tex]\[
5 \cdot 25 = 125
\][/tex]

[tex]\[
x \cdot x^2 = x^{1+2} = x^3
\][/tex]

So the expression inside the cube root becomes:

[tex]\[
125x^3
\][/tex]

Now, simplify [tex]\(\sqrt[3]{125x^3}\)[/tex]:

[tex]\[
\sqrt[3]{125x^3} = \sqrt[3]{125} \cdot \sqrt[3]{x^3}
\][/tex]

We know that:

[tex]\[
\sqrt[3]{125} = 5 \quad \text{(since \(125 = 5^3\))}
\][/tex]
[tex]\[
\sqrt[3]{x^3} = x
\][/tex]

Therefore:

[tex]\[
\sqrt[3]{125x^3} = 5x
\][/tex]

The simplified expression is [tex]\(\boxed{5x}\)[/tex].

Thanks for taking the time to read Simplify tex sqrt 3 5x cdot sqrt 3 25x 2 tex completely A tex 25x 3 tex B tex 25x tex C tex 5x 3. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

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