# Surds and indices Questions

01 September 2023

## What is Surs?

surd is the root of a whole number that has an irrational value and an index number is a number which is raised to a power. The power, also known as the index, tells you how many times you have to multiply the number by itself.

We have provided the selective and important  Surds and indices questions and answers for various Aptitude tests and competitive exams. Try to solve maximum questions to increase your performance in exams.

## Surds and indices Questions WIth Answers

A) 10

B) 7

C) 108

D) 10^7

A) 65/8

B) 0

C) 32

D) 1

E) None of these

A)  10

B) 100

C) 1000

D) 10000

A) 16

B) 2

C) 64

D) 4

### Q5) If 3^(x - y) = 27 and 3^(x + y) = 243, then x is equal to:

A) 0

B) 2

C) 4

D) 6

#### Solution :

3x - y = 27 = 33 x - y = 3 ....(i)

3x + y = 243 = 35 x + y = 5 ....(ii)

On solving (i) and (ii), we get x = 4.

### Q6) The value of (√8)1/3 is:

A) 1

B) 4

C) 2

D) 8

#### Solution :

(√8)1/3 = (81/2)1/3= 81/6 = (23)1/6= 21/2= √2.

### Q7)  If √2n =64, then the value of n is:

A) 2

B) 4

C) 6

D) 12

#### Solution :

√2n =64 => 2n/2 = 64= 26

n/2=6; n=12

### Q8) If 7^(x - y) = 343 and 7^(x + y) = 16807, what is the value of x?

A) 4

B) 3

C) 2

D) 1

#### Solution :

7^(x - y) = 343 = 7^3

=> x - y = 3 ---------------------------(Equation 1)

7^(x + y) = 16807 = 7^5

=> x + y = 5 ---------------------------(Equation 2)

(Equation 1)+ (Equation 2) => 2x = 3 + 5 = 8

=> x = 8⁄2 = 4

### Q9) If 6^m = 46656, What is the value of 6^m-2

A) 36

B) 7776

C) 216

D) 1296

#### Solution :

a^m.a^n=a^m−n

Given that 6m = 46656

6^m−2=6^m/6^2=46656/6^2=46656/36=1296

A) 4

B) 16

C) 64

D) 256.25

#### Solution :

(256)^0.16 x (256)^0.09 = (256)^(0.16 + 0.09)

= (256)^0.25

= (256)^(25/100)

= (256)^(1/4)

= (44)^(1/4)

= 44^(1/4)

= 4^1

= 4