Explain why the square root of a number is defined to be equal to that number to the 1/2 power?

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Answer 1 · 2018-03-13T18:02:29

see below

There are different ways of proving this, but I like this one...

The #sqrt(x)# is defined to be the opposite of #x^2 # meaning that
#sqrt(x^2)=x#

Lets say we don't no the power of the square root jet

#sqrt(x)=x^n#

We do know that #(x^a)^b=x^(a*b)#

Therefore, we can say that

#sqrt(x^2)=x#

#(x^2)^n=x#

#x^(2*n)=x^1#

Now, we can say that #2n=1#

which leads us to #n=1/2#