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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 :

Let's simplify the expression [tex]\(\sqrt[3]{5x} \cdot \sqrt[3]{25x^2}\)[/tex].

To simplify this, we can use the property of exponents which states that the cube root of a product is the product of the cube roots:

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

So, let's apply this property:

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

Now, let's calculate the product inside the cube root:

[tex]\[
5x \cdot 25x^2 = 125x^3
\][/tex]

Now we have:

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

The cube root of [tex]\(125x^3\)[/tex] can be found individually for both the number and the variable:

1. The cube root of 125, which is [tex]\(\sqrt[3]{125} = 5\)[/tex] because [tex]\(5^3 = 125\)[/tex].
2. The cube root of [tex]\(x^3\)[/tex], which is [tex]\(\sqrt[3]{x^3} = x\)[/tex].

Therefore, the cube root of the entire expression is:

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

So, the simplified expression is [tex]\(5x\)[/tex]. The correct answer is [tex]\(5x\)[/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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