Simplify( √(5) )( \sqrt[3]{5} )a. 5 5/6b. 5 1/6c. 5 2/3d. 5 7/6

Question

Simplify
`( √(5) )( \sqrt[3]{5} )`a. 5 5/6b. 5 1/6c. 5 2/3d. 5 7/6

Answer 1

To solve the exercise you can use the following properties of radicals and exponents

`\sqrt[n]{a^m}=a^{(m)/(n)}`
`a^ma^n=a^(m+n)`

So, in this case, you have

`\sqrt[]{5\text{ }}=5^{(1)/(2)}`
`\sqrt[3]{5}=5^{(1)/(3)}`

And finally,

`\sqrt[]{5}\sqrt[3]{5}=5^{(1)/(2)}5^{(1)/(3)}=5^{(1)/(2)+(1)/(3)}=5^{(3+2)/(6)}=5^{(5)/(6)}`

Therefore, the correct answer is A.

`5^{(5)/(6)}`