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Square Roots

Square Roots

The inverse (opposite) operation for squaring is to square root. The square root symbol is shown with a symbol in front of the number being square rooted.

Determining the square root of a number means what number would I have to multiply by itself to get the number I started with? For example, what is `sqrt(49)`? Multiplying 7 x 7 = 49, so `sqrt(49)` = 7.

Note that a square root has two possible answers. A negative multiplied by a negative also gives a positive answer:

+2 x +2 = +4; and

-2 x -2 = +4.

The answer to `sqrt(4)` may be +2 or -2. Sometimes a negative answer can be ignored because it does not make sense.

Note: the square root of a negative number does not exist (except in very advanced mathematics).

Example 1

What is `sqrt(81)`?

9 x 9 = 81, so `sqrt(81)` = 9.

-9 x -9 = +81, so `sqrt(81)` = -9 is also an answer.

Answer: 9 and -9

Example 2

Calculate `sqrt(frac(1)(4))`. Show only the positive value.

`frac(1)(2)` x `frac(1)(2)` = `frac(1)(4)`

Answer: `frac(1)(2)`

See also Inverse Operations