Question

What is the following product? ^3 sqrt 5 x sqrt 2

Answer 1

Explanation:

The answer is 6√200, or option B on edg.

Answer 2

`\sqrt[6]{200}`

Explanation:

We have been an radical expression
`\sqrt[3]{5}* √(2)` and we are asked to find the product of our given expression.

We can write our given numbers as:

`\sqrt[3]{5}=\sqrt[3*2]{5^2}=\sqrt[6]{5^2}`

`√(2)=\sqrt[2]{2}=\sqrt[3*2]{2^3}=\sqrt[6]{2^3}`

Using exponent property
`\sqrt[m]{a}=a^{(1)/(m)}` we can write our expression as:

`(5^2)^{(1)/(6)}* (2^3)^{(1)/(6)}`

Using exponent property
`(a^m)^n=a^(m*n)` we can write our expression as:

`(5^2* 2^3)^{(1)/(6)}`

`(25* 8)^{(1)/(6)}`

`(200)^{(1)/(6)}`

Upon writing our answer as radical we will get:
`\sqrt[6]{200}`

Therefore, the product of our expression will be:
`\sqrt[6]{200}`.