Suppose we have the expression 8/15, with 15 under a square root sign. In order to rationalize this expression, we would multiply this expression by another expression which consists of a numerator and denominator that is identical to the denominator in our original equation. This means that we would multiply 8/15 (keeping in mind that the 15 is under a square root) by 15/15, with each the numerator and the denominator individually under a square root sign. We end up with a numerator which consists of 8 times 15 with a square root over the 15, and a denominator that is 15 without a square root. The reason the denominator that consists merely of 15 has no square root over it is because the square root of 15 times the square root of 15 = 15. Likewise the square root of the product of 15 x 15 = 15.
April 5, 2014