Question

How do you change the expression `5^(1/2)` to radical form?

Answer 1

`5^(1/2)=color(blue)(sqrt(5))`

Explanation:

This is basically a definition:
`color(white)("XXX")b^(1/a)=root(a)(b)`

To see why this is a reasonable definition
consider that in general
`color(white)("XXX")b^(2k)=b^k*b^k`

In the case of `5^(1/2)`
`color(white)("XXX")5=5^1=(5^(1/2))*(5^(1/2))`
that is
`color(white)("XXX")5^(1/2)` must be a value which when multiplied by itself is equal to `5`
and since `sqrt(5)*sqrt(5)=5`, the primary solution to this is
`color(white)("XXX")5^(1/2)=sqrt(5)`