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Squaring numbers math help. How to square negatives, fractions and decimals (x^2)

Updated on March 14, 2013

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:

1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400.

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.

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    jekai urtal 5 years ago

    nice!

  • joanwz profile image

    Joan Whetzel 5 years ago from Katy, Texas

    Great instructions and examples.

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