Mathematics · Quantitative Aptitude

Surds and Indices

362 Questions

Surds and indices questions focus on evaluating square roots, cube roots, and fractional exponents. These topics are a core part of the quantitative aptitude section in many competitive exams. Practicing these problems builds speed and accuracy for solving numerical equations.

Square roots evaluationCube roots calculationExponents and powersFractional exponentsSurds multiplication

Surds and Indices Questions

Multiple choice maths square root square root of perfect square finding square root of a number square root of a perfect square

Subtracting which odd number will get the value of 288 for the square root of the number 484 using repeated subtraction method?

  1. 25

  2. 23

  3. 27

  4. 29
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Repeated subtraction method: Subtract successive odd numbers from the given number starting from 1 till the difference becomes zero.
So, 484 - 1 = 483
483 - 3 = 480
480 - 5 = 475
475 - 7 = 468
468 - 9 = 459
459 - 11 = 448
448 - 13 = 435
435 - 15 = 420
420 - 17 = 403
403 - 19 = 384
384 - 21 = 363
363 - 23 = 340
340 - 25 = 315
315 - 27 = 288 
27 is the odd number, subtracting with 315 to get the value of 288.

Multiple choice maths square root square root of perfect square finding square root of a number square root of a perfect square

From which odd number you will get the value zero, for the square root of the number 64 using repeated subtracting method?

  1. 13

  2. 15

  3. 9

  4. 5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Repeated subtraction method: Subtract successive odd numbers from the given number starting from 1 till the difference becomes zero.
So, 64 - 1 = 63
63 - 3 = 60
60 - 5 = 55
55 - 7 = 48
48 - 9 = 39
39 - 11 = 28
28 - 13 = 15
15 - 15 = 0.
15 is the odd number, we get the value of zero for the square root of the number 64.

Multiple choice maths square root square root of perfect square finding square root of a number square root of a perfect square

Subtracting which odd number will get the value of 144 for the square root of the number 169 using repeated subtraction method?

  1. 3

  2. 5

  3. 7

  4. 9
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Repeated subtraction method: Subtract successive odd numbers from the given number starting from 1 till the difference becomes zero.
So, 169 - 1 = 168
168 - 3 = 165
165 - 5 = 160
160 - 7 = 153
153 - 9 = 144
9 is the odd number, subtracting with 153 to get the value of 144.

Multiple choice maths power and exponent power of powers laws of exponents and powers law of indices

Which of the following expresses the power of quotient rule?

  1. $\left (\dfrac {a}{b}\right )^{m} = \dfrac {a^{m}}{b^{m}}$
  2. $\left (\dfrac {a}{b}\right )^{m} = \left (\dfrac {a}{b}\right )^{m}$
  3. $\left (\dfrac {a}{b}\right )^{m} = \dfrac {a^{m}}{b}$
  4. $\left (\dfrac {a}{b}\right )^{m} = \dfrac {a^{m}}{b^{-m}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If the division of two bases is powered by the same exponent,

 then the result is division of both the bases, 
each powered by the given exponent.
$\therefore \left (\dfrac {a}{b}\right )^{m} = \dfrac {a^{m}}{b^{m}}$
So, option $A$ is correct.

Multiple choice maths power and exponent power of powers laws of exponents and powers law of indices

Evaluate: $\displaystyle \left [ \left ( 4 \right )^{\tfrac{1}{4}}\times \left ( 2 \right )^{\tfrac{1}{2}}\times \left ( 5 \right )^{\tfrac{1}{5}} \right ]^{0}$

  1. $40$
  2. $0$
  3. $1$
  4. $10$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

=$\displaystyle \left [ \left ( 4 \right )^{\tfrac{1}{4}}\times \left ( 2 \right )^{\tfrac{1}{2}} \times \left ( 5 \right )^{\tfrac{1}{2}}\right ]^{0}$

=$\displaystyle 4^{0}\times 2^{0}\times 5^{0}$
=$\displaystyle 1\times 1\times 1$
=$1$
So, option $C$ is correct.