Question

Why any number raised to the power of ½ is its square root?

Answer 1

In taking a square root of 4 for instance, we ask ourselves what number(s) can by multiplied by themselves once in order to give 4? The answer is: well 2 × 2 gives 4 .Thus, if Sqrt is to denote the process of taking the square root we have:

22 = 4

Sqrt(22) = Sqrt(4)

2 = Sqrt (4)

and we say that the "square root of 4 is equal to 2". Same works for the value -2. If you notice above, the Sqrt process actually undoes what the raising to the power of 2 had done; in other words, in some sense this is the "opposite" process of squaring. Recall from our algebraic rules for powers that a number to a power can be raised to a power again and all we do is multiply the powers; then note that the square root process can be written as raising to the power of ½:

Sqrt(22) = (22)½ = 22 × ½ = 21 = 2



Numbers can be raised to fractional powers and our simplest exmple is thattaking the square root of a number is equivalent to raising that number to the power of ½.

Hope it will help u