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# GRE Quantitative Arithmetic – Exponents & Roots

- July 20, 2020
- Posted by: CareerLabs Author
- Category: Free GRE Preparation

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

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