TUTORIALS:

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:
