Squares & Square Roots

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What are squares and square roots?

Squares are a simple form of exponents. The square of a number is the number multiplied by itself, for example:

4 × 4 = 16

It is also written as:

The square root of a number is the inverse of the square.

Thus, , because 4 × 4 =16

Also, note that , because (4) × (4) =16

We write ( means + and -)

For the SAT, the College Board recommends that you know the squares of integers up to 12:

x	1	2	3	4	5	6	7	8	9	10	11	12
x2	1	4	9	16	25	36	49	64	81	100	121	144

And also the square roots:

x	1	4	9	16	25	36	49	64	81	100	121	144
	1	2	3	4	5	6	7	8	9	10	11	12

To square a fraction, multiply the numerator by itself and do the same for the denominator.

Example:

Take note that if a positive fraction which is less than 1 is squared, the result is always smaller than the original fraction.

What are perfect squares?
Perfect squares are numbers that we get when we square an integer.
We can think of square root as the opposite or inverse of squaring. SAT & ACT Math: Using Radicals
Learn how to rationalize a radical.