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Watch the video for an introduction to Square Roots.
Another introduction to Square Roots Video:
Square Roots
Square Roots
Finding the square root of a number is the opposite of a number squared.
For example, the square root of 9 is 3 because 32 = 9.
This would be written using the square root sign (√) as √9 = 3.
√9 = 3 would be read as "the square root of 9 is 3".
Factors
Factors
Another way to find the square root of a number is to find all the factors of the number. You'll remember that factors are all the numbers that divide evenly into it.
For example, the factors of 9 are 1, 3, and 9 because 1 x 9 = 9 and 3 x 3 = 9.
Generally, factors come in pairs:
You can list the factors of 12 as 1, 2, 3, 4, 6, 12
They can be listed as 'factor pairs'.
1 x 12
2 x 6
3 x 4
Whenever a number has 2 identical factors that factor is the square root of the number. So a perfect square will have an odd number of factors.
Here are the factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
1 x 36
2 x 18
3 x 12
4 x 9
6 x 6
Two of the factors are identical; there are 7 different factors (7 is an odd number) so 36 IS a perfect square.
Here are the factors of 50: 1, 2, 5, 10, 25, 50.
1 x 50
2 x 25
5 x 10
No two factors are identical; there are 6 different factors (6 is an even number) so 50 is NOT a perfect square.
Examples
Examples
Example 1:
Find the square root of 25.
Solution:
The factors of 25 are
1 x 25
5 x 5
Because 5 occurs twice, it is the square root of 25.
Example 2:
Is 48 a perfect square?
Solution:
The factors of 48 are 1, 2, 4, 6, 8, 12, 24, 48.
1 x 48
2 x 24
4 x 12
6 x 8
There is an even number of factors and no factor repeats so 48 is not a perfect square.
Modelling square roots
Modelling square roots
Any number that has an odd number of factors will be a perfect square.
You can also demonstrate square roots using a diagram.
This square has an area of 49 square units.
Each side length is √49 = 7 units.
So the square root of 49 is 7.
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