Question

Which of the following best defines 2 2/3?

A:cube root 4
B:square root 4
C:cube root 2
D:square root 2

Answer 1

Option A.

Explanation:

The given expression is

`2^{(2)/(3)}`

We need to find the equivalent expression of given expression.

Using the properties of exponent the given expression can we written as

`(2^2)^{(1)/(3)}`
`[\because (a^m)^n=a^(mn)]`

`4^{(1)/(3)}`

Using the another property of exponent we get

`\sqrt[3]{4}`
`[\because a^{(1)/(n)}=\sqrt[n]{a}]`

The expression cube root 4 is equivalent to the given expression.

Therefore, the correct option is A.

Answer 2

A.
`\sqrt[3]{4}` = Cube root of 4.

Explanation:

We have been given an expression
`2^{(2)/(3)}`. We are asked to find the equivalent expression for our given expression.

Using exponent property
`\sqrt[n]{a^m} =a^{(m)/(n)`, we will get,

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

`2^{(2)/(3)}=\sqrt[3]{4}`

Upon looking at our given choices, we can see that option A is the correct choice.