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# Simplifying Square Roots That Contain Whole Numbers

Example 1

Simplify: Solution The largest perfect square factor of 8 is 4. Write as a product of two radicals. Simplify  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 Write the prime factorization of 108. Group pairs of factors to form perfect squares.  Write as a product of three radicals. Simplify and simplify   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: 