Question

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

Answer 1

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

Answer 2

Answer:

Squaring and square root are inverses, so one should "undo" the other. That is, squaring the square root of a number results in the number. Using the power of a power rule, you multiply the exponents. Since a number to the first power is itself, the product of the exponents must equal 1. This means that the power of the square root must be the reciprocal of 2, or one half.

Step-by-step explanation:

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