Question

PLEASE HELP 50 POINTS

What is the radical form of each of the given expressions?

Drag the answer into the box to match each expression.


2 1/2
2 2/3
3 3/2
3 1/3

Answer 1

Explanation:

The numerator of the exponent becomes an exponent. The denominator of the exponent becomes the index of the root.

`2^{(1)/(2)} = √(2)`

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

`3^{(3)/(2)} = √(3^3)`

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

Answer 2

`2^{(1)/(2)}=√(2)`

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

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

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

Explanation:

First, we need to make some definitions about radical forms.

The expression
`a^{(b)/(c)}` is equivalent to :

`a^{(b)/(c)}=\sqrt[c]{a^(b)}` (I)

Now let's work with the expressions given :

The first one is
`2^{(1)/(2)}`

Using the expression (I) :

`2^{(1)/(2)}=\sqrt[2]{2^(1)}=√(2)`

The second one is
`2^{(2)/(3)}`

Using (I) :

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

The third expression is
`3^{(3)/(2)}`

Using the expression (I) :

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

And the last expression is
`3^{(1)/(3)}`

Using the expression (I) :

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