Question

Select the correct answer. Which expression is equivalent to ^3 square root of 200k^15, if k ≠ 0

Please help I’m in the middle of a test

Answer 1

It is B bc it is in the radical form of ^3sqrt root of 200k^15

Answer 2

The equivalent algebraic expression to $\sqrt[3]{200k^{15}}$ is $2~k^5~\sqrt[3]{25}$

The correct answer is an option (B)

What is algebraic expression?

"It is a mathematical statement which consists of numbers variables and some algebraic operations."

What are exponents?

"It refers to the number of times a number is multiplied by itself."

For given question,

We have been given an algebraic expression $\sqrt[3]{200k^{15}}$

We need to find an equivalent algebraic expression to given expression.

We know that the properties of exponents,

for positive integers a, b, n

$\sqrt[n]{a}=a^{(\frac{1}{n} )}\\\\\sqrt[n]{ab}=a^{(\frac{1}{n} )}b^{(\frac{1}{n} )}$

We can write algebraic expression $\sqrt[3]{200k^{15}}$ as,

$\sqrt[3]{200k^{15}}\\\\=\sqrt[3]{25\times 8\times k^{15}}\\\\=(25)^{\frac{1}{3} }\times (8)^{\frac{1}{3} }\times (k^{15})^{\frac{1}{3} }\\\\=\sqrt[3]{25}\times 2\times (k)^{\frac{15}{3} }\\\\ =2\sqrt[3]{25} \times k^5\\\\=2~k^5~\sqrt[3]{25}$

Therefore, the equivalent algebraic expression to $\sqrt[3]{200k^{15}}$ is $2~k^5~\sqrt[3]{25}$

The correct answer is an option (B)

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