Question

What is the following product

Answer 1

Answer: $\sqrt[6]{200}$

Answer 2

Answer:

Option B.$\sqrt[6]{200}$

Step-by-step explanation:

The given expression is ∛5.√2 and we have to find the product.

In this question ∛5 can be written as $5^{\frac{1}{3} }$ and $\sqrt{2}=2^{\frac{1}{2}}$

We know to multiply these terms we should have the same powers of both the terms.

Now we will convert these terms to the terms having same powers.

first term $5^{\frac{1}{3}}=5^{(\frac{1}{3}).(\frac{2}{2})}$

=$5^{\frac{2}{6}}$

=$25^{\frac{1}{6}}$

Second term √2 = $2^{\frac{1}{2}}$

= $2^{(\frac{1}{2}).(\frac{3}{3})}$

= $2^{\frac{3}{6}}$

= $8^{\frac{1}{6}}$

Now we multiply these terms

$25^{\frac{1}{6}}.8^{\frac{1}{6}}$

= $200^{\frac{1}{6} }$

Therefore option B is the answer.