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 |
x^{2} |
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.
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