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Similarly, you can divide one radical by another by dividing their contents:
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If x is equivalent to the expression shown here, what is the value of
To find the value of x, first simplify
Now, divide the numerator by the denominator and simplify:
Thus,
Therefore, the answer is 11.
Simplifying radicals
In some cases, you can simplify a radical by factoring it and then evaluating one of the factors as a whole number. This is always the case when the value inside the radical is divisible by a square number, such as 4, 9, 16, 25, and so forth.
For example, here are three radicals that can be simplified by factoring out
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Similarly, you can simplify the following three radicals by factoring out
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These three radicals can be simplified by factoring out
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And these three can be simplified by factoring out
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An SAT question may ask you to simplify a radical. For example:
(A)
(B)
(C)
(D)
The number 72 is divisible by 9, so you can factor and simplify
Although
This result is the most simplified form of
