TUTORIALS:
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Simplifying Square Roots That Contain Whole
Numbers
Example 1
Simplify:
![](./articles_imgs/1047/simpli42.gif)
Solution |
![](./articles_imgs/1047/simpli43.gif) |
The largest perfect square factor of 8 is 4.
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![](./articles_imgs/1047/simpli44.gif) |
Write as a product of two radicals.
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![](./articles_imgs/1047/simpli45.gif) |
Simplify
![](./articles_imgs/1047/simpli46.gif) |
![](./articles_imgs/1047/simpli47.gif) |
Thus, in simplified form,
![](./articles_imgs/1047/simpli48.gif)
Note:
In general, 4 is a factor of a number if the
last two digits of the number are divisible
by 4.
For example:
4 is a factor of 236 since 36 is divisible
by 4.
Example 2
Simplify:
![](./articles_imgs/1047/simpli49.gif)
Solution
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![](./articles_imgs/1047/simpli50.gif) |
Write the prime factorization of 108.
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![](./articles_imgs/1047/simpli51.gif) |
Group pairs of factors to form perfect squares.
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![](./articles_imgs/1047/simpli52.gif) |
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![](./articles_imgs/1047/simpli53.gif) |
Write as a product of three radicals.
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![](./articles_imgs/1047/simpli54.gif) |
Simplify
and simplify
![](./articles_imgs/1047/simpli56.gif) |
![](./articles_imgs/1047/simpli57.gif) |
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![](./articles_imgs/1047/simpli58.gif) |
Thus, in simplified form,
![](./articles_imgs/1047/simpli59.gif)
Note:
1) In general, 9 is a factor of a number if the
sum of the digits of the number is divisible
by 9.
For example:
9 is a factor of 198 since 1 + 9 + 8
= 18 and 18 is divisible by 9.
2) If you realize that 36 is the largest perfect
square factor of 108, the you can write:
![](./articles_imgs/1047/simpli60.gif)
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