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Squares & Square Roots




 
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More Lessons for Arithmetic

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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.


 

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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