Answer:
Option B.[tex]\sqrt[6]{200}[/tex]
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 [tex]5^{\frac{1}{3} }[/tex] and [tex]\sqrt{2}=2^{\frac{1}{2}}[/tex]
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 [tex]5^{\frac{1}{3}}=5^{(\frac{1}{3}).(\frac{2}{2})}[/tex]
=[tex]5^{\frac{2}{6}}[/tex]
=[tex]25^{\frac{1}{6}}[/tex]
Second term √2 = [tex]2^{\frac{1}{2}}[/tex]
= [tex]2^{(\frac{1}{2}).(\frac{3}{3})}[/tex]
= [tex]2^{\frac{3}{6}}[/tex]
= [tex]8^{\frac{1}{6}}[/tex]
Now we multiply these terms
[tex]25^{\frac{1}{6}}.8^{\frac{1}{6}}[/tex]
= [tex]200^{\frac{1}{6} }[/tex]
Therefore option B is the answer.
