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

Explanation:

It falls out from the definition of a square root and the rules of exponents.

If r is a square root of x, then ...

  r×r = x

The rules for exponents tell you ...

  (a^b)(a^c) = a^(b+c)

So if r is some power (a) of x, then ...

  r×r = (x^a)(x^a) = x^(a+a) = x^(2a)

but we have said that r×r = x, so ...

  x^(2a) = x = x^1

Equating exponents, we have ...

  2a = 1

  a = 1/2

So ...

  r = x^(1/2) . . . . . the square root of x

linear

step-by-step explanation: