Exponents and roots is one of the topics that GRE tests from your high school knowledge. While the questions from this topic tend to be a little tricky, if you have the required conceptual clarity, getting them right should not be a problem, especially with the GRE techniques by our instructors. Since it might have been a few years since you learnt it, brushing over it might be a good idea in order to boost your score in the GRE Quant Section. 

Exponents and roots, though two different topics, yet are closely related to one another. 

First things first- Understanding Exponents

Exponents represent the repeated multiplication of a number. For example, where 7 is known as the base and 5 as the power. The entire expression is read as 7 to the fifth power or 7 raised to 5 (or 5th power).

When the power is 2, it is known as squaring. When it is three, it is known as cubing.

If a negative number is raised to a power n, the result can be positive or negative depending on whether n is even or odd. If the power of a negative number is even then the resultant value will be positive and negative otherwise. 

Negative Exponents or Zero

Exponents can be negative or zero, and the process of representing these exponents is: 

where p is any non-zero number. If p=0, then the result would be an undefined number.

For all non-zero numbers with negative exponents,

It is important to note that, 

So, what is a square root?

The inverse of an exponent is root. A non-negative number p would have 2 square roots – one positive and one negative.  

For example, 2 and -2 are square roots of 4,  3 and -3 are both square roots of 9, -4 and 4 are  both square roots of 16 and so on.

The symbol used for representing square root is √ , which is known as radical sign. We say that

Higher order roots

The order of square root is 2. For higher order roots of any positive number, the representation is done in a similar way. Cube root is of order 3 whereas, fourth root is of order 4.

Let’s put our knowledge to test:

Question:

Solution:

step 1: Square the given expression, so that roots can be removed. But remember to un-square the result in the end to get the right answer.

step 2: Hence we get the expression as,

step 3: 

step 4: 

step 5: 

step 6: 

step 7:

step 8: We need to un-square it, so, answer will be

 

CareerLabs is glad to help you in your GRE preparation journey. You can ask for any assistance related to GRE from us by just giving a missed call at +91 6366004441. You can also write to us at support@thecareerlabs327512368.wpcomstaging.com