# Surds and Indices Questions

Surds and indices questions are a crucial and integral part of major competitive examinations held in India such as CAT, SSC CGL, banking exams, and surds and indices questions are included in these premier competitive examinations to gauge the critical thinking, problem-solving and analytical ability of the candidates appearing for competitive exams. In this blog, we will cover surds and indices questions in a detailed manner.

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## Important Concepts and Formula to Solve Surds and Indices Questions

There are some crucial concepts and formulae with regard to surds and indices which must be crystal clear enough to crack the surds and indices questions asked in the competitive exams

### Formulae of Indices

• In mathematics, an index (indices) is the power or exponent raised to a number or variable. In number 2², for example, 2 is the index of 2.
• aˣ * bª = abˣ⁺ª
• bˣ/bª= bˣ⁻ª
• (bˣ)ª=bˣª
• b⁻ˣ =1/bˣ
• bº= 1 (where b is not equal to 0)
• (cd)ˣ=cˣ * dˣ

### Formulae of Surds

• Surds are square roots (√) of numbers that cannot be reduced to a whole or rational number. A fraction cannot accurately represent it. Consider the following example: √2 1.414213(approx)
• d√b + e√b = (d + e)√b
• f√b – o√b = (f – o)√b
• √df = √d * √f
• √(k/d) = √k/√d
• Note-Surds are irrational numbers but not all irrational numbers are surds

Also ReadMaths For Competitive Exams

## Surds and Indices: Important Questions

Some of the most frequently asked questions from the surds and indices section are mentioned below which you must practice for acing your exam

Q1 (17)3.5 *(17)? = (17)8

1. 7.8
2. 4.5
3. 9
4. 2.8

Q2 If (a/b) x-1= (b/a) x-3

1. 2
2. 2/8
3. 7/9
4. 2/9

Correct Answer is D)2/9

Q3 Given that 100.48 = x, 100.70= y, and xª = y², then the value of a is close to:

1. 2.9
2. 3.9
3. 4.1
4. 1.0

Correct Answer is A) 2.9

Q4 If 5ª = 3125, then the value of 5(ª⁻³) is:

1. 5
2. 6
3. 9
4. 2

Q5 (0.04)⁻¹˙⁵

1. 125
2. 55
3. 100
4. 25

Q6 (25)⁷˙⁵ * (5)²˙⁵ / (125)¹˙⁵ = (5)?

1. 15
2. 13
3. 17
4. 19

Q7  3√2 -2√3/3√2+2√3 + √12/√3-√2

1. 11
2. 12
3. 2
4. 15

Correct Answer A) 11

Q8 4⁶¹ + 4⁶² + 4⁶³ + 4⁶⁴ is divisible by

1. 12
2. 16
3. 17
4. 11

Q9 5²ⁿ⁻²=625,find n

1. 3
2. 8
3. 0
4. 1

Correct Answer is A) 3

Q10 If 17ⁿ=4913,then find the value of 2²ⁿ⁻¹ٰ

1. 32
2. 28
3. 16
4. 12

Correct Answer is A) 32

Q11 If 5²ⁿ = 51625 ,then find the value of n²

1. 9
2. 27
3. 33
4. 99

Correct Answer is A) 9

Q12 If 7(x – y) = 343 and 7(x + y) = 16807, what is the value of x?

1. 4
2. 5
3. 8
4. 7

Correct Answer is A) 4

This was all about Surds and Indices Questions which will definitely help you out in acing the surds and indices section in the competitive examination. Hope you found the blog to be insightful and informative! Are you ready to kickstart your study abroad journey? Our experts and counselors at Leverage Edu are just a call away to provide you end-to-end support with your application process. Sign up for a free session today!