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Square Roots
Square Roots
Definition —
Square Root
For a nonnegative real number, a, the principal square root of a is
written
 If b is a nonnegative real number and b2
= a, then
Example:
 because 7 is nonnegative and 72
= 49.
We can use geometry to provide a visual interpretation of a positive square
root.
For example, suppose a square has an area of 25 square inches. The length
of each side is the principal square root of the area. That is,
the length of a side of the square =
 = 5 inches.
A perfect square is a number that has a rational square root.
As we work with square roots, we will find it helpful to recognize perfect
squares and their square roots. The table lists some whole number perfect
squares and their principle square roots.
To approximate the square root of a number that is not a perfect square, we
can estimate or use the
 key on a calculator.
| Perfect Squares |
Principal Square Roots |
| 02 = 0 |
 |
| 12 = 1 |
 |
| 22 = 4 |
 |
| 32 = 9 |
 |
| 42 = 16 |
 |
| 52 = 25 |
 |
| 62 = 36 |
 |
| 72 = 49 |
 |
| 82 = 64 |
 |
| 92 = 81 |
 |
| 102 = 100 |
 |
 |
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Property — Squares and Square Roots
English Squaring and taking a square root “undo” each other.
Algebra If a is a nonnegative real number, then
Example
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