Surds and indices

09 May 2020


 A 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.


Problems on Surds and Indices

Q1) Evaluate 1000^7 / 10^14 = ?

A) 10

B) 7

C) 108

D) 10^7

Solution :


Q2) 43/2 + 4-3/2 = ?

A) 65/8

B) 0

C) 32

D) 1

E) None of these

Solution : 


Q3) If a and b are positive integers such that a^b = 121 then (a-1)^(b + 1) = ?

A)  10

B) 100

C) 1000

D) 10000

Solution :


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Q4) (256)^0.16 x (256)^0.09 = ?

A) 16

B) 2

C) 64

D) 4

Solution :


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 

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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 

Q10) (256)^0.16 x (256)^0.09 = ? 

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 

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