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

9514 1404 393

  (x^(1/2))^2 = x^(2/2) = x

Step-by-step explanation:

The square root of a number, when multiplied by itself, gives the original number.

  (√x)(√x) = x

The rule for exponents is that powers of the same base, when multiplied, will be the base to the sum of those powers.

  (a^b)(a^c) = a^(b+c)

Also, the first power of a number is that number itself.

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