- Education and Science
Squaring numbers math help. How to square negatives, fractions and decimals (x^2)
The First 12 Square Numbers Video
To work out the square of a number just multiply the number by itself. A little 2, written on the top right of the number, means that you are squaring the number.
So, 7² means you need to work out the square of 7 which is:
7 × 7 = 49 (not 7 × 2, which is a common error)
Similarly, 15² means you need to work out the square of 15 which is:
15 × 15 = 225 (again not 15 × 2)
If you are squaring a negative number, then this can be worked out in a similar way.
For example (-3)² means the square of -3 which is:
-3 × -3 = 9 (two negative make a plus)
Finding a square of a fraction can also be done in a similar process.
For example, work out the square of 3/4.
(3/4)² = ¾ × ¾ = 9/16 (just multiply the numerators and denominators together).
Decimals, can also be squared in the same way.
Work out 0.3².
This means 0.3×0.3 = 0.09
It’s also a good idea that you remember your first 10 (or 20) square numbers as square numbers are popular questions on math tests. The first 20 square numbers are:
If you are working larger square numbers then you can use your calculator.
Work out 142².
On you calculator you can type in 142 × 142 = 20164. Alternatively, you can use the square key on your calculator (x²).
The opposite process to squaring a number is square rooting. A square root sign looks like √. For example, work out the square root of 121. If you look at the square numbers listed above, 121 is the 11th square number in the list, so the √121 = 11 (since 11 multiplied by 11 is 121). You can also work out the square root of larger number on your calculator by using the square root key (which looks like√).
So to summarise, remember that squaring means multiply the number by itself and don’t just multiply the number by 2!. Also, a square root is the inverse process to squaring.