Question

Explain why `sqrt(a)` is the same thing as `a^(1/2)` ?

So nobody that I have asked so far understands this Algebra question. Can you figure it out for me?

Answer 1

They are the same thing only written differently.

Explanation:

In order to solve problems, sometimes mathematicians change different roots into the form:

`root(color(green)n)a rarr a^(1/color(green)n)`

Examples of actual roots would be:

`sqrta rarr a^(1/color(red)2)`

`root(color(blue)3)a rarr a^(1/color(blue)3)`

`root(color(orange)4)a rarr a^(1/color(orange)4`

Instead of saying "square root of `a`", it's like saying "`a` raised by `1/2` power". And "cube root of `a`" is the same as saying "`a` raised by `1/3` power".

It simply is written in a different way, but it means the same thing.

Since you have `sqrta` it will equal `a^(1/color(red)2)`. A normal `sqrt` sign is dividing it into `2` squares, so you will have a `2` in the power.