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TUTORIALS:
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Simplifying Square Roots That Contain Whole
Numbers
Example 1
Simplify:
| Solution |
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| The largest perfect square factor of 8 is 4.
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| Write as a product of two radicals.
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Simplify
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Thus, in simplified form,
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:
| Solution
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| Write the prime factorization of 108.
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| Group pairs of factors to form perfect squares.
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| Write as a product of three radicals.
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Simplify
 and simplify
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Thus, in simplified form,
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:
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