Simplifying square roots
When you simplify square roots write down:
|
2 |
= |
√4 |
|
3 |
= |
√9 |
|
4 |
= |
√16 |
|
5 |
= |
√25 |
|
6 |
= |
√36 |
|
7 |
= |
√49 |
|
8 |
= |
√64 |
|
9 |
= |
√81 |
|
10 |
= |
√100 |
Find the biggest square that
divides the number in the root.
Examples
1. Simplify
√108
Write down what we know:
2=√4, 3=√9, 4=√16
5=√25, 6=√36, 7=√49
The biggest square that divides into 108 is 36
√108=√3×36
And if we write out what we know from multiplying surds
√9×√9=3×3=9=√81=√9×9
Therefore √3×36=√3×√36
√3×√36=√3×6=6√3
Answer: √108=6√3
2. Simplify
√45
Write down what we know
2=√4, 3=√9, 4=√16
5=√25, 6=√36, 7=√49
The biggest square that divides 45 is 9
√45=√9×5
And if we write down what we know from multiplying surds
√9×√9=3×3=9
=√81=√9×9
Therefore √45=√9×5=√9×√5
√9×√5=3√5
Answer: √45=3√5
3. Simplify
√80
Write down what we know
2=√4, 3=√9, 4=√16
5=√25, 6=√36, 7=√49
The biggest square that divides 80 = 4
(It is actually 16 but this example shows you that you can simplify again)
√80=√4×20
And if we write down what we know from multiplying surds
√9×√9=3×3=9
=√81=√9×9
Therefore √80=√4×20=√4×√20
=2×√20
But √20 can be simplified
The biggest square that divides 20 = 4
2×√20=2×√4×5
And if we write down what we know from multiplying surds
√9×√9=3×3=9
=√81=√9×9
Therefore 2×√4×5=2×√4×√5
=2×2×√5
2×2×√5=4√5
Answer: √80=4√5
