- Home
- Allegations and Mixtures
- AP GP HP
- Arithmetic Progressions
- Averages
- Boats and Streams
- Geometric Progressions
- Harmonic Progressions
- Clocks
- Calendar
- Clocks and Calendars
- Compound Interest
- Simple Interest
- Simple Interest and Compound Interest
- Linear Equations
- Quadratic Equations
- Co-ordinate geometry
- Perimeter Area Volume
- Divisibility
- HCF and LCM
- HCF
- LCM
- Number System
- Percentages
- Permutations Combinations
- Combinations
- Piipes and Cisterns
- Probability
- Work and Time
- Succesive Discounts
- Heights and Distance
- Decimals and Fractions
- Logarithm
- Venn Diagrams
- Geometry
- Set Theory
- Problem on Ages
- Inverse
- Surds and Indices
- Profit and Loss
- Speed, Time and Distance
- Algebra
- Ratio & Proportion
- Number, Decimals and Fractions






Please login

Prepinsta Prime
Video courses for company/skill based Preparation

Prepinsta Prime
Purchase mock tests for company/skill building
How To Solve Surds And Indices Questions Quickly
How to Solve Surds and Indices Questions Quickly
The natural number which cannot be expressed in the form of fraction known as Surds. For example: \sqrt{2} and the Indices refers to the power to which a number is raised. For example: 2²

How to Solve Surds and Indices Ques. Quickly :
- Surds: Number which cannot be expressed in the fraction form of two integers is called as surd. For example: \sqrt{2}
- Indices: Indices refers to the power to which a number is raised. For example; 2²
Sample Solutions Regarding the Rules of Surds and Indices :
Indices Multiplication rules:-
- Multiplication rule with same base
a ^n ⋅ a*m = a^(m + n)
Example:
2^3 ⋅ 2^4 = 2^(3+4) = 2^7 = 2⋅2⋅2⋅2⋅2⋅2⋅2 = 128
Surds Multiplication rules:-
- Multiplication rule with same indices
a^n ⋅ b^n = (a ⋅ b)^n
Example:
3^2 ⋅ 2^2 = (3⋅2)^2 = 36
Indices Division rules:-
- Division rule with same indices
a^n / b^m = (a / b)^n
Example: 93 / 33 = (9/3)3 = 27
Surds Division rules:-
- Division rule with same base
a^m / a^n = a^(m – n)
Example: 3^5 / 3^3 = 3^(5-3) = 9
Surds and Indices Power rules
Power rule 1
- (a^n)^m = a^(n.m)
Example:
(2^3)^2 = 2^(3⋅2) = 2^6 = 2⋅2⋅2⋅2⋅2⋅2 = 64
Power rule 2
- (a^n)^m = a^(n^m)
Example:
(2^3)^2 = 2^(3^2) = 2^(3⋅3) = 2^9 = 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2 = 512
Power rule 3
- n√a =a^1/n
Example:
27^1/3 = 3√27 = 3
Type 1: How to Solve Surds and Indices Quickly- Simplify the expression
Question 1. Find the value of 7-25 – 7-26
Options:
A. 6 × 7-26
B. 6 × 7-25
C. 7 × 7-25
D. 7 × 7-26
Solution: 7-25 – 7-26 = \frac{1}{7^{25}} – \frac{1}{7^{26}}
\frac{7 – 1}{7^{26}} = 6 × 7-26
Correct option: A
Question 2. Simplify (256) /mathbf{^ \frac{3}{4}}
Options:
A. 16
B. 12
C. 256
D. 64
Solution: (256)^ \frac{3}{4} = (44)^ \frac{3}{4}= 43 = 64
Correct option: D
Question 3. Find the value of 8112 ÷ 8110
Options:
A. 72
B. 64
C. 81
D. 49
Solution: We know,
\frac{a^m}{a^n} = am-n
= 8 (112 – 110) = 82 = 64
Correct option: B
Type 2: Solve Surds and Indices Quickly- Find the value of x
Question 1. If 4x + 4x + 1 = 80, then the value of xx is
Options:
A. 16
B. 9
C. 25
D. 4
Solution: 4x(1 + 4) = 80
4x * 5 = 80
4x = \frac{80}{5}
4x = 16
x = 2
xx = 22 = 2
Correct option: D
Question 2. If 2a = 3 \sqrt{32}, then a is equal to:
Options:
A. \frac{1}{3}
B. 4
C. \frac{5}{3}
D. \frac{1}{2}
Solution: Given value 2a
3 \sqrt{32}
2a = (32)^ \frac{1}{3}
2a = (25)^ \frac{1}{3}
2a = (2)^ \frac{1}{3}
a = \frac{5}{3}
Correct option: C
Question 3. If x and y are whole numbers such that xy = 169, then find the value of (x – 1)y + 1
Options:
A. 1331
B. 2744
C. 1728
D. 729
Solution: 169 = 132
So, the value of x = 13 and y = 2
Now, (x – 1)y + 1
= (13 – 1)2+1
= (12)3
=1728
Correct option: C
Read Also – Formulas to solve surds & indices questions
Excellent