# 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.

Also Read: List of Banking Courses

## 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

## 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

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

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

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

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

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

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

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