Square of a Number

Squaring a number means to multiply that number by itself.

The notation for squaring a number (x) is as follows: x2

When squaring an integer, the result obtained is called a perfect square.

When preparing for the test, make sure that you are fully capable of understanding and reproducing the following table, as well as recognizing the numbers that are perfect squares and perfect cubes.

n

n2

n3(n > 0)

n3(n < 0)

1

1

1

-1

2

4

8

-8

3

9

27

-27

4

16

64

-64

5

25

125

-125

6

36

216

-216

7

49

You will not need to know any higher

You will not need to know any higher

8

64

9

81

10

100

11

121

12

144

Squared numbers and special properties

􀁹 x2 > 0 always, except for x = 0

􀁹 x2 > x for x > 1

􀁹 x2 < x for 0 < x < 1 *important

􀁹 x2 = x for x = 1 or 0

􀁹 The square root of x2 equals the absolute value of x.

􀁹 If x2 = y2, then either x = y, or y = -x, or x = -y.

The following is an example:

Of the following numbers, which is a both a perfect square and a perfect cube?

A. 4

B. 8

C. 9

D. 16

E. 64

Note: the answer is (E)