Quantitative Aptitude - Square Roots and Cube Roots - Formula & Concepts Quiz

 =

• 1]

  232

• 2]

  123

• 3]

  432

• 4]

  543

Square root of 64009 is

• 1]

  253

• 2]

  347

• 3]

  363

• 4]

  803

Evaluate -

• 1]

  3

• 2]

  5

• 3]

  6

• 4]

  6.4

The square root of (272²−128²) is

• 1]

  144

• 2]

  200

• 3]

  240

• 4]

  256

Find the square root of 3 upto three decimal places

• 1]

  1.732

• 2]

  2.732

• 3]

  1.222

• 4]

  1.414

The digit in the units place in the square root of 15876 is 

• 1]

  8

• 2]

  6

• 3]

  4

• 4]

  2

If ​=.0026, the square root of 67,60,000 is:

• 1]

  1/26

• 2]

  26

• 3]

  260

• 4]

  2600

Three fifth of the square of a certain number is 126.15, What is the number?

• 1]

  210.25

• 2]

  75.69

• 3]

  14.5

• 4]

  145

  simplifies to:

• 1]

  4/3

• 2]

  1/2

• 3]

  3/4

• 4]

  5/3

Find the cube root of 2744.

• 1]

  14

• 2]

  13

• 3]

  12

• 4]

  11

If x=.and y= find value of  is

• 1]

  13

• 2]

  14

• 3]

  15

• 4]

  16

By what least number 4320 be multiplied to obtain a number which is a perfect cube?

• 1]

  35

• 2]

  48

• 3]

  50

• 4]

  62

If \(3a = 4b = 6c   \)  and \(a + b + c = 27\sqrt {29} { \text{,}}   \) then\( \sqrt {{a^2} + {b^2} + {c^2}} \)is ?

• 1]

  \(3\sqrt {29} \)

• 2]

  81

• 3]

  87

• 4]

  None of these

The square root of \({ \text{0}}{ \text{.}}\overline { \text{4}} \)  is ?

• 1]

  \(0.\overline 6 \)

• 2]

  \(0.\overline 7 \)

• 3]

  \(0.\overline 8 \)

• 4]

  \(0.\overline 9 \)

\(\sqrt {0.2} = ?\)

• 1] 0.02
• 2] 0.2
• 3] 0.447
• 4] 0.632

The value of \(\sqrt {0.121} \)   is = ?

• 1] 0.011
• 2] 0.11
• 3] 0.347
• 4] 1.1

The value of \(\sqrt {\frac{{0.16}}{{0.4}}} \)   is = ?

• 1] 0.02
• 2] 0.2
• 3] 0.63
• 4] None of these

The value of \(\frac{{1 + \sqrt {0.01} }}{{1 - \sqrt {0.1} }}\)   is close to = ?

• 1] 0.6
• 2] 1.1
• 3] 1.6
• 4] 1.7

The square root of 535.9225 is = ?

• 1] 23.15
• 2] 23.45
• 3] 24.15
• 4] 28.25

If 1537* is a perfect square, then the digit which replace * is = ?

• 1] 2
• 2] 4
• 3] 5
• 4] 6

If \(\sqrt 5 = 2.236{ \text{,}}\)   then the value of \(\frac{1}{{\sqrt 5 }} \) is = ?

• 1] 0.367
• 2] 0.447
• 3] 0.745
• 4] None of these

If \(\sqrt {24} = 4.889,\)   the value of \(\sqrt {\frac{8}{3}} \)   is = ?

• 1] 0.544
• 2] 1.333
• 3] 1.633
• 4] 2.666

If \(\sqrt 6 = 2.449{ \text{,}}\)   then the value of \(\frac{{3\sqrt 2 }}{{2\sqrt 3 }}\)   is = ?

• 1] 0.6122
• 2] 0.8163
• 3] 1.223
• 4] 1.2245

If \({ \text{ }}2*3 = \sqrt {13} \)   and 3 * 4 = 5, then the value of 5 * 12 is ?

• 1]

  \(\sqrt {17} \)

• 2]

  \(\sqrt {29} \)

• 3]

  12

• 4]

  13

The least perfect square number divisible by 3, 4, 5, 6 and 8 is = ?

• 1] 900
• 2] 1200
• 3] 2500
• 4] 3600

The least number by which 294 must be multiplied to make it a perfect square, is = ?

• 1] 2
• 2] 3
• 3] 6
• 4] 24

What is the least number which should be subtracted 0.000326 in order to make it a perfect square = ?

• 1] 0.000002
• 2] 0.000004
• 3] 0.02
• 4] 0.04

What is the least number to be added to 7700 to make it a perfect square ?

• 1] 77
• 2] 98
• 3] 131
• 4] 221
• 5] None of these

The smallest number to be added to 680621 to make the sum a perfect square is = ?

• 1] 4
• 2] 5
• 3] 6
• 4] 8

The greatest four digit perfect square number is = ?

• 1] 9000
• 2] 9801
• 3] 9900
• 4] 9981

The least number of 4 digits which is a perfect square is = ?

• 1] 1000
• 2] 1016
• 3] 1024
• 4] 1036

Given \(\sqrt 5 = 2.2361,   \sqrt 3 = 1.7321{ \text{,}}   then \frac{1}{{\sqrt 5 - \sqrt 3 }}\)   is equal to ?

• 1] 1.98
• 2] 1.984
• 3] 1.9841
• 4] 2

\(\frac{1}{{\left( {\sqrt 9 - \sqrt 8 } \right)}} -   \frac{1}{{\left( {\sqrt 8 - \sqrt 7 } \right)}} +   \frac{1}{{\left( {\sqrt 7 - \sqrt 6 } \right)}} -   \frac{1}{{\left( {\sqrt 6 - \sqrt 5 } \right)}} +   \frac{1}{{\left( {\sqrt 5 - \sqrt 4 } \right)}}\)   is equal to ?

• 1]

  0

• 2]

  1/3

• 3]

  1

• 4]

  5

Determined the value of \(\frac{1}{{\sqrt 1 + \sqrt 2 }}{ \text{ + }}  \frac{1}{{\sqrt 2 + \sqrt 3 }} +   \frac{1}{{\sqrt 3 + \sqrt 4 }} +   ...... +   \frac{1}{{\sqrt {120} + \sqrt {121} }}{ \text{ = ?}}\)

• 1]

  8

• 2]

  10

• 3]

  \(\sqrt {120} \)

• 4]

  \(12\sqrt 2 \)

If \(\sqrt 2 = 1.414{ \text{,}}   \) the square root of \(\frac{{\sqrt 2 - 1}}{{\sqrt 2 + 1}}\)  is nearest to = ?

• 1] 0.172
• 2] 0.414
• 3] 0.586
• 4] 1.414

Given that \(\sqrt 3 = 1.732{ \text{,}}   \)  the value of \(\frac{{3 + \sqrt 6 }}{{5\sqrt 3 - 2\sqrt {12} - \sqrt {32} + \sqrt {50} }}\)    is ?

• 1] 1.414
• 2] 1.732
• 3] 2.551
• 4] 4.899

\(\left( {\frac{{2 + \sqrt 3 }}{{2 - \sqrt 3 }} + \frac{{2 - \sqrt 3 }}{{2 + \sqrt 3 }} + \frac{{\sqrt 3 - 1}}{{\sqrt 3 + 1}}} \right) \)     simplifies to = ?

• 1]

  \(16 - \sqrt 3 \)

• 2]

  \(4 - \sqrt 3 \)

• 3]

  \(2 - \sqrt 3 \)

• 4]

  \(2 + \sqrt 3 \)

If \(x = 3 + \sqrt 8 ,   \) then \({x^2} + \frac{1}{{{x^2}}}\) is equal to = ?

• 1] 30
• 2] 34
• 3] 36
• 4] 38

If \(a = \frac{{\sqrt 3 + \sqrt 2 }}{{\sqrt 3 - \sqrt 2 }},   b = \frac{{\sqrt 3 - \sqrt 2 }}{{\sqrt 3 + \sqrt 2 }}\)   then the value of \({a^2} + {b^2}\)   would be = ?

• 1] 10
• 2] 98
• 3] 99
• 4] 100

If \(a = \frac{{\sqrt 5 + 1}}{{\sqrt 5 - 1}}   \) and \(b = \frac{{\sqrt 5 - 1}}{{\sqrt 5 + 1}},\)   the value of \(\left( {\frac{{{a^2} + ab + {b^2}}}{{{a^2} - ab + {b^2}}}} \right)\)   is ?

• 1]

  3/4

• 2]

  4/3

• 3]

  3/5

• 4]

  5/3

One-fourth of a herd of camels was seen in the forest. Twice the square root of the herd had gone to mountains and the remaining 15 camels were seen on the bank of a river. Find the total number of camels ?

• 1] 32
• 2] 34
• 3] 35
• 4] 36

The number of trees in each row of a garden is equal to the total number of rows in the garden. After 111 trees have been uprooted in a storm, there remain 10914 trees in the garden. The number of rows of trees in the garden is = ?

• 1] 100
• 2] 105
• 3] 115
• 4] 125

1250 oranges were distributed among a group of girls of a class. Each girl got twice as many oranges as the number of girls in that group. The number of girls in the group was = ?

• 1] 25
• 2] 45
• 3] 50
• 4] 100

A mobile company offered to pay the Indian Cricket Team as much money per run scored by the side as the total number it gets in a one-dayer against Australia. Which one of the following cannot be the total amount to be spent by the company in this deal ?

• 1] 21904
• 2] 56169
• 3] 101761
• 4] 121108

\(1728 \div \root 3 \of {262144} \times ? - 288\)      = 4491

• 1] 148
• 2] 156
• 3] 173
• 4] 177

\(99 \times 21 - \root 3 \of ? = 1968\)

• 1] 1367631
• 2] 111
• 3] 1366731
• 4] 1367

\( \root 3 \of {\sqrt {0.000064} } = ?\)

• 1] 0.02
• 2] 0.2
• 3] 2
• 4] None of these

Value of \(\sqrt {0.01} \times \root 3 \of {0.008} - 0.02 \)    is = ?

• 1] 0
• 2] 1
• 3] 2
• 4] 3

The value of \({ \text{ }} \root 3 \of {\frac{{0.2 \times 0.2 \times 0.2 + 0.04 \times 0.04 \times 0.04}}{{0.4 \times 0.4 \times 0.4 + 0.08 \times 0.08 \times 0.08}}} \)        is ?

• 1] 0.125
• 2] 0.25
• 3] 0.5
• 4] 0.75

By what least number must 21600 be multiplied so as to make it perfect cube ?

• 1] 6
• 2] 10
• 3] 20
• 4] 30

What is the smallest number by which 3600 be divided to make it a perfect cube ?

• 1] 9
• 2] 50
• 3] 300
• 4] 450

Which smallest number must be added to 710 so that the sum is a perfect cube ?

• 1] 11
• 2] 19
• 3] 21
• 4] 29

Solved \( \root 4 \of {{{\left( {625} \right)}^3}} = ?\)

• 1]

  \( \root 3 \of {1875} \)

• 2]

  25

• 3]

  125

• 4]

  None of these

If \(\sqrt y = 4x{ \text{}}   \) then \(\frac{{{x^2}}}{y}\) is = ?

• 1]

  2

• 2]

  1/16

• 3]

  1/4

• 4]

  4

\(9{x^2} + 25 - 30x\)    can be expressed as the square of = ?

• 1]

  \(3{x^2} - 25\)

• 2]

  3x + 5

• 3]

   - 3x - 5

• 4]

  3x - 5

If \(\sqrt {33} = 5.745{ \text{}}\)   then which of the following values is approximately \(\sqrt {\frac{3}{{11}}} { \text{ ?}}\)

• 1] 1
• 2] 6.32
• 3] 0.5223
• 4] 2.035

If \(a = \frac{{\sqrt 3 }}{2}{ \text{}}\)   then \(\sqrt {1 + a} + \sqrt {1 - a} = ?\)

• 1]

  \(\left( {2 - \sqrt 3 } \right)\)

• 2]

  \(\left( {2 + \sqrt 3 } \right)\)

• 3]

  \(\left( {\frac{{\sqrt 3 }}{2}} \right)\)

• 4]

  \(\sqrt 3 \)

What is \(\frac{{5 + \sqrt {10} }}{{5\sqrt 5 - 2\sqrt {20} - \sqrt {32} + \sqrt {50} }}\)      equal to ?

• 1]

  5

• 2]

  \(5\sqrt 2 \)

• 3]

  \(5\sqrt 5 \)

• 4]

  \(\sqrt 5 \)

The square root of \(\frac{{{{\left( {0.75} \right)}^3}}}{{1 - 0.75}} { \text{ + }}\left[ {0.75 + {{\left( {0.75} \right)}^2} + 1} \right]\)    is = ?

• 1] 1
• 2] 2
• 3] 3
• 4] 4

The cube root of .000216 is:

• 1] .6
• 2] .06
• 3] 77
• 4] 87

What should come in place of both x in the equation \(\frac{x}{{\sqrt {128} }} = \frac{{\sqrt {162} }}{x}\)

• 1] 12
• 2] 14
• 3] 144
• 4] 196

The least perfect square, which is divisible by each of 21, 36 and 66 is:

• 1] 213444
• 2] 214344
• 3] 214434
• 4] 231444

\(\sqrt {1.5625} = ?\)

• 1] 1.05
• 2] 1.25
• 3] 1.45
• 4] 1.55

If \(3\sqrt 5 + \sqrt {125} \)   = 17.88, then what will be the value of \(\sqrt {80} + 6\sqrt 5 ?\)

• 1] 13.41
• 2] 20.46
• 3] 21.66
• 4] 22.35

If a = 0.1039, then the value of \(\sqrt {4{a^2} - 4a + 1} + 3a\)     is:

• 1] 0.1039
• 2] 0.2078
• 3] 1.1039
• 4] 2.1039

If \(x = \frac{{\sqrt 3 + 1}}{{\sqrt 3 - 1}}   \)  \(y = \frac{{\sqrt 3 - 1}}{{\sqrt 3 + 1}}\)and then the value of \(\left( {{x^2} + {y^2}} \right)\)   is?

• 1] 10
• 2] 13
• 3] 14
• 4] 15

A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:

• 1] 57
• 2] 67
• 3] 77
• 4] 87

The square root of \(\left( {7 + 3\sqrt 5 } \right)  \left( {7 - 3\sqrt 5 } \right)\)   is

• 1]

  \(\sqrt 5 \)

• 2]

  2

• 3]

  4

• 4]

  \(3\sqrt 5 \)

If \(\sqrt 5 = 2.236, \)   then the value of \(\frac{{\sqrt 5 }}{2} - \frac{{10}}{{\sqrt 5 }} + \sqrt {125} \)   is equal to :

• 1] 5.59
• 2] 7.826
• 3] 8.944
• 4] 10.062

\(\left( {\frac{{\sqrt {625} }}{{11}} \times \frac{{14}}{{\sqrt {25} }} \times \frac{{11}}{{\sqrt {196} }}} \right){\kern 1pt} \)     is equal to :

• 1] 5
• 2] 6
• 3] 8
• 4] 11

\(\sqrt {0.0169 \times ?} = 1.3\)

• 1] 10
• 2] 100
• 3] 1000
• 4] None of these

\({\left( {\sqrt 3 - \frac{1}{{\sqrt 3 }}} \right)^2}\) simplifies to:

• 1]

  3/4

• 2]

  \(\frac{4}{{\sqrt 3 }}\)

• 3]

  4/3

• 4]

  None of these

How many two-digit numbers satisfy this property. : The last digit (unit's digit) of the square of the two-digit number is 8 ?

• 1] 1
• 2] 2
• 3] 3
• 4] None of these

The square root of 64009 is:

• 1] 253
• 2] 347
• 3] 363
• 4] 803

The square root of 41209 is equal to = ?

• 1] 103
• 2] 203
• 3] 303
• 4] 403

The square root of 123454321 is = ?

• 1] 111111
• 2] 12341
• 3] 11111
• 4] 11211

The number of digits in the square root of 625685746009 is = ?

• 1] 4
• 2] 5
• 3] 6
• 4] 7

\(\sqrt {\sqrt {17956} + \sqrt {24025} } = ?\)

• 1] 19
• 2] 155
• 3] 256
• 4] 289
• 5] None of these

One-fourth of the sum of prime numbers, greater than 4 but less than 16, is the square of = ?

• 1] 3
• 2] 4
• 3] 5
• 4] 7

\(\sqrt {176 + \sqrt {2401} } \)    is equal to = ?

• 1] 14
• 2] 15
• 3] 18
• 4] 24

\({\left( {15} \right)^2} + {\left( {18} \right)^2} - 20 = \sqrt ? \)

• 1] 22
• 2] 23
• 3] 529
• 4] 279841
• 5] None of these

\(\sqrt ? \times \sqrt {484} = 1034\)

• 1] 2025
• 2] 2209
• 3] 2304
• 4] 2401
• 5] None of these

\(\sqrt {11881} \times \sqrt ? = 10137\)

• 1] 8281
• 2] 8649
• 3] 9216
• 4] 9409
• 5] None of these

In the equation \(\frac{{4050}}{{\sqrt x }} = 450{ \text{}}\)   the value of x is = ?

• 1] 9
• 2] 49
• 3] 81
• 4] 100

\(\sqrt {\frac{{16}}{{25}}} \times \sqrt {\frac{?}{{25}}} \times \frac{{16}}{{25}} = \frac{{256}}{{625}}\)

• 1] 5
• 2] 8
• 3] 16
• 4] None of these

The square root of \(\left( {{{272}^2} - {{128}^2}} \right) \)  is = ?

• 1] 144
• 2] 200
• 3] 240
• 4] 256

If y = 5,   then what is the value of \(10y\sqrt {{y^3} - {y^2}} \)   = ?

• 1]

  \(50\sqrt 2 \)

• 2]

  100

• 3]

  \(200\sqrt 5 \)

• 4]

  500

\(\sqrt {\frac{{25}}{{81}} - \frac{1}{9}} = ?\)

• 1]

  2/3

• 2]

  4/9

• 3]

  16/81

• 4]

  25/81

\({\left[ {{{\left( {\sqrt {81} } \right)}^2}} \right]^2} = {\left( ? \right)^2}\)

• 1] 8
• 2] 9
• 3] 4096
• 4] 6561
• 5] None of these

The digit in the unit's place in the square root of 15876 is = ?

• 1] 2
• 2] 4
• 3] 6
• 4] 8

Which of the following is closest to \(\sqrt 3 = ?\)

• 1]

  1.69

• 2]

  173/100

• 3]

  1.75

• 4]

  9/5

What percentage of the numbers from 1 to 50 have squares that end in the digit 1 ?

• 1] 1%
• 2] 5%
• 3] 10%
• 4] 11%
• 5] 20%

While solving a mathematical problem, Samidha squared a number and then subtracted 25 from it rather than the required i.e., first subtracting 25 from the number and then squaring it. But she got the right answer. What was the given number ?

• 1] 13
• 2] 38
• 3] 48
• 4] Cannot be determined
• 5] None of these

How many perfect squares lie between 120 and 300 ?

• 1] 5
• 2] 6
• 3] 7
• 4] 8

The number of perfect square numbers between 50 and 1000 is = ?

• 1] 21
• 2] 22
• 3] 23
• 4] 24

A man born in the first half of the nineteenth century was x years old in the year x2. He was born in ?

• 1] 1806
• 2] 1812
• 3] 1825
• 4] 1836

R is a positive number. It is multiplied by 8 and then squared. The square is now divided by 4 and the square root is taken. The result of the square root is Q. What is the value of Q ?

• 1] 3R
• 2] 4R
• 3] 7R
• 4] 9R

The smallest natural number which is a perfect square and which ends in 3 identical digits lies between ?

• 1] 1000 and 2000
• 2] 2000 and 3000
• 3] 3000 and 4000
• 4] 4000 and 5000

If the product of four consecutive natural numbers increased by a natural number p, is a perfect square, then the value of p is = ?

• 1] 1
• 2] 2
• 3] 4
• 4] 8

The value of \(\sqrt {0.000441} \)  is = ?

• 1] 0.00021
• 2] 0.0021
• 3] 0.021
• 4] 0.21

\({1.5^2} \times \sqrt {0.0225} = ?\)

• 1] 0.0375
• 2] 0.3375
• 3] 3.275
• 4] 32.75

The value of \(\sqrt {0.01} { \text{ + }} \sqrt {0.81} { \text{ + }} \sqrt {1.21} { \text{ + }} \sqrt {0.0009} \)  is = ?

• 1] 2.03
• 2] 2.1
• 3] 2.11
• 4] 2.13

Given that \(\sqrt {13} = 3.605\)   and \(\sqrt {130} = 11.40\)  . find the value of \(\sqrt {1.30} \)  + \(\sqrt {1300}\)  + \(\sqrt {0.0130} \)   = ?

• 1] 36.164
• 2] 36.304
• 3] 37.164
• 4] 37.304

If = the value of x is = ?

• 1] 52
• 2] 58
• 3] 62
• 4] 68

For what value of * the statement  = 1 is true?

• 1] 15
• 2] 25
• 3] 35
• 4] 45

Which number should replace both the question marks in the following equation ?/1776=111/?

• 1] 343
• 2] 414
• 3] 644
• 4] 543
• 5] None of these

Which number can replace both the question marks in the equation =?

• 1]

  12

• 2]

  7

• 3]

  

• 4]

  None of these

What should come in place of both the question marks in the equation x/√128 = √162/x ?

• 1] 12
• 2] 14
• 3] 144
• 4] 196

If √x+x/y  = x√x/y  where x and y are positive real numbers, then y is equal to ?

• 1]

  x + 1

• 2]

  x - 1

• 3]

  x² + 1

• 4]

  x² - 1

Given \(\sqrt 2 = 1.414.\)   Then the value of \(\sqrt 8\)  + \(2\sqrt {32} \)  -  \(3\sqrt {128}\)  + \(4\sqrt {50}\)   is = ?

• 1] 8.426
• 2] 8.484
• 3] 8.526
• 4] 8.876

The approximate value of \(\frac{{3\sqrt {12} }}{{2\sqrt {28} }} \div \frac{{2\sqrt {21} }}{{\sqrt {98} }}\)  is ?

• 1] 1.0605
• 2] 1.0727
• 3] 1.6007
• 4] 1.6026

\(\sqrt {110.25} \times \sqrt {0.01} \div \)    \(\sqrt {0.0025}\)  - \(\sqrt {420.25}\)  equals ?

• 1] 0.50
• 2] 0.64
• 3] 0.73
• 4] 0.75

  is equal to ?

• 1] 0.9
• 2] 0.99
• 3] 9
• 4] 99

The value of     is ?

• 1]

  0.1

• 2]

  10

• 3]

  \({10^2}\)

• 4]

  \({10^3}\)