The Square Numbers

When an integer is multiplied by itself, the resulting product is called a square number.

The square of 3 is 3\times 3=3^{2}

=9

The square of 1 is 1^{2}=1\times 1

=1

The square number of -5 is \left( -5\right) ^{2}

=25

The square of 1.5 is 1.5^{2}=1.5\times 1.5

=2.25

The first few square numbers are:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, …


Square Numbers


The square of a number is the result of multiplying the number by itself. So, the square of 3 is 3×3,written as 3^2, which is equal to 9. The square of -4 is -4\times -4,written as ({ -4) }^{ 2 }, which is 16.

The first few squares of the integers are

On the other hand, the square root of a number, written √number, is the number we has before squaring. Since { 3 }^{ 2 }=9, we say \sqrt { 9 } =3. But -3\times -3 is also equal to 9, so \sqrt { 9 } =\pm 3.
\sqrt { 1 } =\pm 1
\sqrt { 4 } =\pm 2
\sqrt { 9 } =\pm 3
\sqrt { 16 } =\pm 4, and so on.