Mathematics · Quantitative Aptitude

Surds and Indices

408 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

The square root of $42\, \displaystyle \frac{583}{1369}$ is :

  1. $6\, \displaystyle \frac{19}{37}$
  2. $4\, \displaystyle \frac{2}{11}$
  3. $7\, \displaystyle \frac{2}{121}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\sqrt{42\, \displaystyle \cfrac{583}{1369}}\, =\, \sqrt{\displaystyle \cfrac{58081}{1369}}$
$=\, \displaystyle \cfrac{\sqrt{58081}}{\sqrt{1369}}$
$=\, \displaystyle \cfrac{241}{37}\, =\, 6\, \displaystyle \cfrac{19}{37}$

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

If $\sqrt{49}=7$, then find the value of $\sqrt{49}+\sqrt{0.49}+\sqrt{0.0049}+\sqrt{0.000049}$

  1. 7777

  2. 77.77

  3. 777.7

  4. 7.777
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$\sqrt{49}+\sqrt{0.49}+\sqrt{0.0049}+\sqrt{0.000049}\=7+\sqrt { \displaystyle\frac { 49 }{ 100 }  } +\sqrt {\displaystyle \frac { 49 }{ 10000 }  } +\sqrt { \displaystyle\frac { 49 }{ 1000000 }  } \ =7+\displaystyle\frac { \sqrt { 49 }  }{ \sqrt { 100 }  } +\displaystyle\frac { \sqrt { 49 }  }{ \sqrt { 10000 }  } +\displaystyle\frac { \sqrt { 49 }  }{ \sqrt { 1000000 }  } \ =7+\displaystyle\frac { 7 }{ 10 } +\displaystyle\frac { 7 }{ 100 } +\displaystyle\frac { 7 }{ 1000 } \ =7+0.7+0.07+0.007\ =7.777$

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

Find the square roots of $100\;and\;169$ by method of repeated substraction.

  1. $10; 13$
  2. $10; 17$
  3. $20; 13$
  4. $20; 17$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For $\sqrt{100}$
$100-1=99$
$99-3=96$
$96-5=91$
$91-7=84$
$84-9=75$
$75-11=64$
$64-13=51$
$51-15=36$
$36-17=29$
$19-19=0$

For $\sqrt{169}$
$169-1=168$
$168-3=165$
$165-5=160$
$160-7=153$
$153-9=144$
$144-11=133$
$133-13=120$
$120-15=105$
$105-17=88$
$88-19=69$
$69-21=48$
$48-23=25$
$25-25=0$
From $100\;and\;169$ we have substracted successive odd numbers starting from $1$ and obtained $0$ at $10th\;and\;13th$ steps, respectively.
So, $\sqrt{100}=10\;and\;\sqrt{169}=13$. 

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

Find the square root of $100$ by the method of repeated substraction.

  1. $10$.
  2. $11$
  3. $9$
  4. $12$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

We know that the sum of the first n odd natural numbers is $n^{2}$
From $100$, we subtract successive odd numbers starting from $1$ as under
$100-1=99\;\;\;99-3=96$
$96-5=91\;\;\;\;91-7=84$
$84-9=75\;\;\;\;75-11=64$
$64-13=51\;\;\;51-15=36$
$36-17=19\;\;\;19-19=0$
and obtain $0$ at $10th$ step.
$\therefore\;\sqrt{100}=10$.
From $169$, we subtract successive odd numbers starting from $1$ as under
$169-1=168\;\;\;168-3=165$
$165-5=160\;\;\;\;160-7=153$
$153-9=144\;\;\;\;144-11=133$
$133-13=120\;\;\;120-15=105$
$105-17=88\;\;\;88-19=69$
$69-21=48\;\;\;48-23=25$
$25-25=0$
and obtain $0$ at $13th$ step.
$\therefore\;\sqrt{169}=13$.





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

Complete the repeated subtraction to find the square root of $225$.

  1. $9$
  2. $45$
  3. $25$
  4. $15$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

$225 -1 = 224$ ,

$224 -3 = 221 $,
$221-  5 = 216$, 
$216 -7 = 209$,
$209 - 9= 200$ ,
$200 -11 = 189$
$189-  13 = 176$ , 
$176-  15 = 161$, 
$161 -17 = 144$,
$144- 19 = 125$
$125 - 21 = 104 $
$ 104-  23 = 81 $
$81-  25 = 56$
$ 56-  27 = 29$, 
$29 -29 = 0 = 15$ 
Therefore, D is the correct answer.

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.