How Do You Rationalize Denominators? When radicals have values that are not perfect squares, it means they are irrational expressions. We will eradicate such values if we are rationalizing the divisor. If we have a value 4/√6 so, rationalize the denominator by following steps: Step#1: Multiply the divisor by a radical that will discard it entirely. What we do when we have a square root in the denominator? We will multiply the square root by a perfect square of the radical in the denominator. In the case, the radicand value is imperfect square then, you will multiply it by itself to find the perfect square. How can you achieve this by multiplying both divisor and numerator by the square root of six? Mathematically. 1. 4/ &radic 6 × √6 / √6 2. 4√6 / √36 -> here, we have a perfect square in the bottom value under the square root. Step#2: Check you have simplified all radicals or not. Step#3: Simplify the fraction as per the demand for example. 4√6 / √36 Here, sq. root 36 is equal to 6. 5√6/6 Here, we will divide numbers without square root by 2 so, the answer will be. 2√6/3 Try to simplify such fractions carefully. We cannot solve the values in the radical unless you solve the outside one. It would be easy to solve without mistakes.

With these problems you will be given an irrational number (such as the square root of three) as a denominator of a fraction. This is just another approach to this skill, in general. The first step is to multiply the top (numerator) and bottom (denominator) of the fraction by the radical itself. Then you just simplify away the radical first followed by the fraction. You will also be faced with multiply terms on the top or bottom. In those cases you just have extra operations to perform, but the basic procedure for rationalizing should remain the same. We work with flat rationalizations that mimic denominators that we will often use in geometric figures. Students should already be familiar with reciprocals, conjugates, and expressions.