SOLUTION: Rationalize the denominator: 8 - radical 2 divided by 6

SOLUTION: Rationalize the denominator: 8 - radical 2 divided by 6 - 3 square root 2

Question 135224: Rationalize the denominator:
8 - radical 2 divided by 6 - 3 square root 2
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The trick is to multiply the fraction by 1 in the form of the conjugate of the denominator divided by itself.

If you have an expression of the form , then its conjugate is , and vice versa of course.

Here your denominator expression is , so the conjugate is , so you need to multiply your original fraction by 1 in the form of

Notice that multiplying a binomial times its conjugate is the reverse of factoring the difference of two squares -- so the result is the first term squared minus the second term squared. Just use FOIL on the numerator expressions:

The result is a fraction with a rational number in the denominator, hence the name of the process.
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