CAT Questions | Indices & Surds

The topic Indices and Surds is a part of the Number System vertical of the Quantitative Aptitude section in the MBA entrance exam. Although we can observe from the trend that the frequency of occurrence of questions in this topic has decreased, we cannot ignore this topic entirely as we can always expect 1-2 questions on this topic in many MBA exams.

Exams which use contain this topic:

Many exams ask questions on Indices and Surds. These may range from 1-2 questions which are usually assigned easy to moderate level of difficulty. Hence, it is wise to cover this topic to score well.


ExamYearNo of QuestionsLevel of Difficulty


List of concepts for Indices and Surds:

Indices: The base ‘a’ raised to power ‘b’ is equal to the multiplication of a, b times a = a × a… × a b times. Where a is the base and b is the indices.


2^1 = 2

2^2 = 2*2 = 4

2^3 = 2*2*2 = 8

Surds: Numbers that can be written as √a + √b, where a and b are not perfect squares and natural numbers. Hence, the numbers in the form of √5, 5√7, ……. x√y

Rules and Properties of Indices and Surds

Name of the Rule



am/ an = am-n

an / bn = (a / b)n


an am = am+n

an  bn = (a b)n


(an)m = anm

anm = a(nm)

m√(an) = a n/m

n√a = a1/n

a-n = 1 / an

Important points to Remember:

1) Surd nx can be simplified if the factor of x is a perfect square
2)Any number raised to the power zero always equals one. (Eg: x 0 = 1)
3) The conjugate of (x√a + y√b) is (x√a – y√b)
4) If the denominator in a fraction has a surd, then rationalize the denominator by multiplying both numerator and denominator by a conjugate surd
5) Different expressions can be simplified by rationalizing the denominator and eliminating the surd
6) Every surd is an irrational number.

Some Questions from Previous Papers

CAT 2019 Slot 1 – If m and n are integers such that (√2)^19 * 3^4 * 4^2 * 9^m * 8^n = 3^n * 16^m (4√64) then m is?

1. -20

2. -24

3. -16

4. -12 

Answer – 12


Given, √2^19 3^4 4^2 9^m 8^n=3^n 16^m ∜64

Or 2^(19/2)×3^4×2^4×3^2m×2^3n= 3^n×2^4m×2^(6/4)

2^(19/2+4+3n)×3^(4+2m)=3^n×2^((4m+6/4) )

Comparing both sides,

n = 4+2m

19/2 +4 + 3n = 4m + 6/4

Or (19 + 8)/2 + 3(4+2m) = 4m + 3/2

27/2 + 12 + 6m = 4m + 3/2

6m -4m = 3/2 – 27/2 -12

2m = -24

Thus m = -12


If 17x = 4913, find the value of 22x-1.

a) 16

b) 32

c) 64

d) 128

17x = 4913

⇒17x = 4913

⇒17x = (17)3

⇒x = 3


Value of 22x-1 ⇒ 22.3-1⇒ 25 = 32


If 2x × 8(1/4) = 2(1/4) then find the value of x

As bases are not equal we cannot add the indices, hence first convert all the numbers with the same base.

2x × (23)(1/8) = 2(1/4)


Law of Indices (xm)n = xmn

 2x × 2(3/4) = 2(1/4)

 2[x + (3/4)] = 2(1/4)

If 4 (x – y) = 64 and 4 (x + y) = 1024, then find the value of x.

a. 3

b. 1

c. 6

d. 4 

4 (x – y) = 64

4 (x – y) = 64 = 43

Equation 1) x – y = 3


4 (x + y) = 1024 = 45

Equation 2) x + y = 5

Solving equation (1) and (2), we get

x = 4 and y = 1


Crosscheck the answers by substituting the values of x and y in the given expression.

4 (4 – 1) = 43 = 64 and 4 (4 + 1) = 45 = 1024

Hence, the answers x = 4 and y = 1 are correct.


If a and b are whole numbers such that ab = 121, then find the value of (a – 1)b + 1

a. 0

b. 10

c. 102

d. 103

121 = 112 , hence value of a = 11 and b = 2 can be considered.

Therefore, the value of (a – 1)b + 1 = (11 – 1) 2 + 1= 103

How to deal with that topic preparation

Preparing for Indices and Surds will require a basic understanding of the key concepts and speedy calculation along with hard work and dedication. Here are some Level-wise preparatory guidelines to follow:

Level – 1

  1. Learn all the basic concepts of indices and surds and their rules and properties.
  2. Learn Speed calculation: For an effective and quick calculation, be thorough with tables till 20, memorize squares till 30, and cubes till 15.
  3. Memorize the properties of the log.
  4. Practice beginner-level questions.

Level – 2

  1. Move on to more complex problems, attempt beginner and intermediate level mock on concepts of Indices and Surds.
  2. Solve previous year CAT questions on Indices and Surds and time yourself. Do not get stuck on one question and try to solve easy questions first.
  3. Keep attempting mocks to check your performance.
  4. Topic-wise mocks, provided by MBAP, can be utilized to enhance your performance.

Level – 3

  1. For advanced level preparation, start practicing questions from the book – How to Prepare for Quantitative Aptitude for the CAT, authored by Arun Sharma.
  2. Questions in Arun Sharma are categorized into Level of Difficulty (LOD), based upon your preparation level, start attempting 3 or 4 questions daily.

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