Multiplying a number by itself gives the **square** of a number.

Instead of writing 4 x 4, it is written as 4^{2}: the little 2 is an **index** and means that the 4 should be multiplied by itself. This is read as 4 *squared*.

Any number can be squared. Squaring a negative number will result in a positive number (minus times a minus is a plus):

-1.6^{2} = -1.6 x -1.6 = +2.56.

Squaring a number smaller than 1 will result in an even smaller number:

0.3^{2} = 0.3 x 0.3 = 0.09.

Fractions can also be squared: (`frac(1)(2)`)^{2} = `frac(1)(2)` x `frac(1)(2)` = `frac(1)(4)`.

Calculate 12^{2}.

12^{2} = 12 x 12 = 144

Answer: 144

Calculate 0.05^{2}.

Work out as 5 x 5 = 25. There are 2 sets of 2 decimal places in the original numbers: there are therefore 4 decimal places in the answer.

Answer: 0.0025

See also Square Sequences

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