Question

Instructions: Determine which expressions can be simplified and if not, explain why not. If yes, simplify completely or rewrite as a simplified radical expression. Must show all work.Last expression that I wasn’t able to include in the picture is (x^4 y) 2/3

Answer 1

`\sqrt[]{5}`

As 5 is a prime number, it is not in the power of 2. Then, the expression cannot be simplified,

______________________

`\sqrt[3]{8}`

Prime factorization of 8 is:

`\begin{gathered} 8=2*2*2 \\ 8=2^3 \end{gathered}`

Then, the expression can be simplified to get;

`\sqrt[3]{8}=\sqrt[3]{2^3}=2`

_________________-

`\sqrt[]{3+5}`

To simplify the expression first add numbers, and then use the prime factorization of result as follow:

`=\sqrt[]{8}=\sqrt[]{2^3}=\sqrt[]{2^2*2}=2\sqrt[]{2}`

_____________

`\sqrt[\square]{(2x)/(3y)}`

As both parts of the fraction under the root are not power of two and both are prime numbers the expression cannot be simplified.

___________________-

`(x^4y)^(2/3)`

Use the next property to rewrite the expression:

`a^(n/m)=\sqrt[m]{a^n}`
`(x^4y)^(2/3)=\sqrt[3]{(x^4y)^2}`

Expand the expression under the root and then simplifiy the expression as follow:

`=\sqrt[3]{x^8y^2}=\sqrt[3]{x^6^{}x^2y^2}=x^2\sqrt[3]{x^2y^2}`