Question

Which radical expression is equivalent to 5^2/3?

sqrt 125

^3 sqrt 5

^3 sqrt 25

sqrt 5

Answer 1

The answer is the last expression. 5^2/3 means you square the five then find the cubic root. 5 squared is equal to 25. Then you find the cubic root. 

Answer 2

Answer:
`\sqrt[3]{25}` is equivalent to the given expression.

Explanation:

Given expression,
`5^(2/3)`

we can write,
`5^(2/3)` =
`(5^2)^(1/3)` (because,
`a^(mn)= (a^m)^n`)

⇒
`5^(2/3)` =
`(25)^(1/3)`

⇒
`5^(2/3)` =
`\sqrt[3]{25}`

(because,we can write,
`x^(1/n)=\sqrt[n]{x}`)