This is a free lesson from our course in Algebra II This lesson explains how to divide square roots radicals and rationalize the denominator. Dividing square roots is similar to simplifying a fraction to lowest terms. For all radicals whose denominators are not equal to 0, divide coefficients, divide radicands, and simplify it. If there is a square root in the denominator of the fraction, you need to simplify by multiplying both the numerator and denominator by the square root that is in the denominator. It may be noted this step will not change the value of the fraction; only its form is changed. This is called 'rationalizing the denominator'.To rationalize take the radical from the denominator, multiply the numerator and denominator by the radical as it appears in the denominator. E.g. 3/ 5 on simplification, yields 3 5/5. (More text below video...)
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(Continued from above) If there is a binomial radical expression E.g. (a + b c) in the denominator, we will multiply by the conjugate.
To find the conjugate of (a + b c) switch the sign between them. For example, 5/(4 + 2 3) simplifies to (10 - 5 3)/2.