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?

1 Answer
Apr 26, 2018

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.