It has been observed that the students while preparing for the GMAT Quantitative section face a lot of problems while dealing with square roots, especially when they have to divide using square roots.

GMAT follows a standard mathematical convention, according to which we should not leave square roots in the denominator of a fraction. For example, √5/2 is acceptable but 2/√5 is not acceptable. This fraction needs to be further simplified to become an acceptable GMAT answer choice. To remove the square roots from the denominator, we rationalize the denominator.

Firstly, to rationalize the denominator, we must multiply the numerator and denominator of the fraction by the same number, which usually is the denominator itself. Thus, to simplify 2/√5 further, we multiply it by the square root of 5 over square root of 5.

But in some cases, dividing by square root becomes complex when denominator involves adding or subtracting a square root. For example, consider the following fraction:

This particular fraction is not acceptable, and it requires further rationalization. But if we multiply the denominator by itself, it will lead to a more complicated expression involving square root. Therefore, instead of multiplying the numerator and denominator by denominator itself we should multiply the expression by the conjugate of the denominator.

We create the conjugate of the denominator by changing the sign in the denominator, like in the above expression conjugate of the denominator is:

Therefore in order to rationalize the above expression, we should multiply both the numerator and the denominator by the given conjugate.

The process for the same is as follows:

Now, we can see that the simplification has removed the square roots from the denominator and the end result is a rationalized and simplified version of the original.

Let’s practice a few questions now.

Solution:

First of all we will isolate ‘k’.

As we know, this form is not acceptable; hence, we need to rationalize the denominator. So, we need to multiply both numerator and denominator by conjugate of the denominator. This will result in:

2. A square and an equilateral triangle each have a side of length 5.What is the ratio of the area of the square to the area of the triangle?

Solution:

The inclusion of square root sign in the denominator makes it incorrect. Therefore, we need to rationalize it.

Answer is (C) .

In Conclusion, we can say that handling square roots in GMAT is not a difficult task if handled with proper care and after understanding the required gradients and parameters. So, always remember whenever you get square roots in the denominator of a fraction, then you have to rationalize the denominator. You can follow the process as explained above to save time and energy. There are two things that can help any student get a good score on the GMAT – proper time management and proper practice of the tested techniques.

*Blog By:*

Sagar Madaan