In rationalizing the denominator, our goal is to get no roots in the bottom of a fraction. In order to do this, we usually multiply the top and bottom both by the bottom (this is a clever form of one) so the radical product in the denominator will become a rational number. In these examples, the denominators are sums and differences of radicals, so we multiply top and bottom by the conjugate of the bottom. If done correctly, there will be no more roots in the denominator.
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