Why does #sqrtx=x^(1/2)#?

1 Answer
Aviv S.
Feb 17, 2018

The reason this is true is that fractional exponents are defined that way.

For example, #x^(1/2)# means the square root of #x#, and #x^(1/3)# means the cube root of #x#. In general, #x^(1/n)# means the #n#th root of #x#, written #root(n)(x)#.

You can prove it by using the law of exponents:

#x^(1/2)*x^(1/2)=x^((1/2+1/2))=x^1=x#

and

#sqrtx*sqrtx=x#

Therefore, #x^(1/2)=sqrtx#.

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