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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 :

We start with the expression

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

Using the property of cube roots that

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

we combine the two cube roots into one:

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

Next, we multiply the radicands:

[tex]$$
(5x)(25x^2) = 125x^3.
$$[/tex]

Thus, the expression becomes

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

Now, we notice that [tex]$125$[/tex] is a perfect cube since [tex]$125 = 5^3$[/tex], and [tex]$x^3$[/tex] is a perfect cube as well. Therefore, we can separate the cube root:

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

So, the completely simplified form 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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