We appreciate your visit to 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. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Sure! Let's simplify the expression [tex]\(\sqrt[3]{5x} \cdot \sqrt[3]{25x^2}\)[/tex] step by step.
1. Combine the cube roots: According to the property of exponents, [tex]\(\sqrt[3]{a} \cdot \sqrt[3]{b} = \sqrt[3]{a \cdot b}\)[/tex]. Therefore, we can combine the two cube roots into one:
[tex]\[
\sqrt[3]{5x} \cdot \sqrt[3]{25x^2} = \sqrt[3]{(5x) \cdot (25x^2)}
\][/tex]
2. Multiply the terms inside the cube root: Now, multiply the terms inside:
[tex]\[
5x \cdot 25x^2 = (5 \cdot 25) \cdot (x \cdot x^2) = 125x^3
\][/tex]
3. Take the cube root of the product: Next, calculate the cube root of the product:
[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 x because [tex]\((x)^3 = x^3\)[/tex].
4. Result: Combine these results:
[tex]\[
\sqrt[3]{125x^3} = 5x
\][/tex]
Therefore, the simplified expression is [tex]\(5x\)[/tex].
The correct answer is [tex]\(5x\)[/tex].
1. Combine the cube roots: According to the property of exponents, [tex]\(\sqrt[3]{a} \cdot \sqrt[3]{b} = \sqrt[3]{a \cdot b}\)[/tex]. Therefore, we can combine the two cube roots into one:
[tex]\[
\sqrt[3]{5x} \cdot \sqrt[3]{25x^2} = \sqrt[3]{(5x) \cdot (25x^2)}
\][/tex]
2. Multiply the terms inside the cube root: Now, multiply the terms inside:
[tex]\[
5x \cdot 25x^2 = (5 \cdot 25) \cdot (x \cdot x^2) = 125x^3
\][/tex]
3. Take the cube root of the product: Next, calculate the cube root of the product:
[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 x because [tex]\((x)^3 = x^3\)[/tex].
4. Result: Combine these results:
[tex]\[
\sqrt[3]{125x^3} = 5x
\][/tex]
Therefore, 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!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
