What is the following product

Question

asked Jul 23, 2018 47.3k views

2 Answers

Yeseanul · Answer 1 · 2018-07-29T12:21:45+0000

Answer:

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

Explanation:

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

In this question ∛5 can be written as
$5^{(1)/(3) }$ and
$√(2)=2^{(1)/(2)}$

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
$5^{(1)/(3)}=5^{((1)/(3)).((2)/(2))}$

=
$5^{(2)/(6)}$

=
$25^{(1)/(6)}$

Second term √2 =
$2^{(1)/(2)}$

=
$2^{((1)/(2)).((3)/(3))}$

=
$2^{(3)/(6)}$

=
$8^{(1)/(6)}$

Now we multiply these terms

$25^{(1)/(6)}.8^{(1)/(6)}$

=
$200^{(1)/(6) }$

Therefore option B is the answer.