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Quantitative Aptitude

SQUARE ROOT AND CUBE ROOT MCQs

Square Roots, Cube Roots, Squares And Square Roots

Total Questions : 547 | Page 27 of 55 pages
Question 261.

`3sqrt(4 12/125)`  =   ?


  1.    `1 2/5`
  2.    `1 3/5`
  3.    `1 4/5`
  4.    `2 2/5`
 Discuss Question
Answer: Option B. -> `1 3/5`

`3sqrt(4 12/125)` =  `3sqrt(512/125)` =  `((8xx8xx8)/(5xx5xx5))^(1/3)` =   `8/5` =  `1 3/5`


Question 262.

The cube root of .000216 is :


  1.    .6
  2.    .06
  3.    .006
  4.    None of these
 Discuss Question
Answer: Option B. -> .06

`(.000216)^(1/3)` =  `((216)/(10^6))^(1/3)` =  `((6 xx 6 xx6)/(10^2 xx 10^2 xx10^2))^(1/3)`

= `(6)/(10^2)` =  `6/100` =  .06



Question 263.

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


  1.    57
  2.    67
  3.    77
  4.    87
 Discuss Question
Answer: Option C. -> 77

Money collected = (59.29 x 100) paise=  5929 paise.

`:.`   Number of members = `sqrt(5929)` = 77.


Question 264.

If a = `(sqrt(5) + 1)/(sqrt(5) - 1)` and b= `(sqrt(5) - 1)/(sqrt(5) +1)` , the value of `((a^2 + ab + b^2)/(a^2 - ab + b^2))`

is


  1.    `3/4`
  2.    `4/3`
  3.    `3/5`
  4.    `5/3`
 Discuss Question
Answer: Option B. -> `4/3`

a = `(sqrt(5) + 1)/(sqrt(5) - 1)`  x `(sqrt(5) + 1)/(sqrt(5) +1)` = `((sqrt(5) + 1)^2)/((5 - 1))`

= `(5 + 1 + 2sqrt(5))/(4)` =  `((3 + sqrt(5))/(2))`

b= `(sqrt(5) - 1)/(sqrt(5) +1)`  x  `(sqrt(5) - 1)/(sqrt(5) -1)` = `((sqrt(5)  - 1)^2)/((5 - 1))` = `(5 + 1 - 2sqrt(5))/(4)`

= `((3 - sqrt(5))/(2))`

`:.`  `a^2 + b^2` = `((3 + sqrt(5))^2)/(4)` + `((3 - sqrt(5))^2)/(4)` = `((3 + sqrt(5))^2 +(3 - sqrt(5))^2)/(4)`

`(2(9 + 5))/(4)`   = 7.

Also, ab = `((3 + sqrt(5) (3 - sqrt(5))/(2)`  = ` (9 - 5)/4` = 1

`:.` ` (a^2 + ab + b^2)/(a^2 - ab + b^2)` =   `((a^2 b^2) + ab)/((a^2 + b^2) - ab)`  =  `(7 + 1)/(7 - 1)` = `8/6` = `4/3`



Question 265.

If `x = (sqrt(3) + 1)/(sqrt(3) - 1)` and ` y = (sqrt(3) - 1)/(sqrt(3) + 1)` then the value of `(x^2 + y^2)` is


  1.    10
  2.    13
  3.    14
  4.    15
 Discuss Question
Answer: Option C. -> 14

`x` = `((sqrt(3) + 1))/((sqrt(3) - 1))  xx ((sqrt(3) + 1))/((sqrt(3) +1)) ` = `((sqrt(3) + 1)^2)/((3 - 1 ))`

 = `(3 + 1 + 2sqrt(3))/(2)` = 2 + `sqrt(3)`

y = `((sqrt(3) - 1))/((sqrt(3)+1))  xx ((sqrt(3) -1))/((sqrt(3)-1)) ` = `((sqrt(3) - 1)^2)/((3 - 1))`

= `(3 + 1 -  2sqrt(3))/(2)` =   `2 - sqrt(3)`

`:.`  `x^2 + y^2` = ` (2 + sqrt(3))^2 + (2 - sqrt(3))^2` =   2(4 + 3) = 14.



Question 266.

If ` x =  (7 - 4sqrt(3))`,  then the value of `(x + 1/x)` is :


  1.    `3sqrt(3)`
  2.    `8sqrt(3)`
  3.    14
  4.    `14 + 8sqrt(3)`
 Discuss Question
Answer: Option C. -> 14

`x + 1/x` = `(7 - 4sqrt(3)) + (1)/((7 - 4sqrt(3)))  xx ((7 + 4sqrt(3)))/((7 + 4sqrt(3)))`

=` (7 - 4sqrt(3)) + ((7 + 4sqrt(3)))/((49 - 48))`

=`(7 - 4sqrt(3)) + (7 + 4sqrt(3))`   = 14



Question 267.

`((2 + sqrt(3))/(2 - sqrt(3))  + (2  - sqrt(3))/(2 + sqrt(3))  + (sqrt(3) - 1)/(sqrt(3) + 1) )` simplifies to :


  1.    `16 - sqrt(3)`
  2.    `4 - sqrt(3)`
  3.    `2 - sqrt(3)`
  4.    `2 + sqrt(3)`
 Discuss Question
Answer: Option A. -> `16 - sqrt(3)`

Given exp.  `(2 + sqrt(3))/(2 - sqrt(3))  xx (2 + sqrt(3))/(2 +sqrt(3))  + (2  - sqrt(3))/(2 + sqrt(3))  xx  (2 -sqrt(3))/(2 - sqrt(3))   + (sqrt(3) - 1)/(sqrt(3) + 1) xx   (sqrt(3) - 1)/(sqrt(3) + 1) `         

=`(( 2 + sqrt(3))^2)/(4 - 3)  + ((2 - sqrt(3))^2)/((4 - 3))  + ((sqrt(3) - 1)^2)/((3 - 1))`

=`[(2 + sqrt(3))^2 + (2 - sqrt(3))^2]  + (4 -2sqrt(3))/(2)`

=` 2(4 + 3) + 2 - sqrt(3)`        = `16 - sqrt(3)`                                         



Question 268.

`(3 + sqrt(6))/(5sqrt(3) - 2sqrt(12) - sqrt(32)  + sqrt(50))` =  ?


  1.    3
  2.    `3sqrt(2)`
  3.    6
  4.    None of these
 Discuss Question
Answer: Option D. -> None of these

Given exp. =  `(3 + sqrt(6))/(5sqrt(3) - 4sqrt(3) - 4sqrt(2)  + 5sqrt(2))`  = `((3 + sqrt(6)))/((sqrt(3) + sqrt(2)))`

= `((3 + sqrt(6)))/((sqrt(3) + sqrt(2)))`  x  `((sqrt(3) - sqrt(2)))/((sqrt(3) - sqrt(2)))`

=`(3sqrt(3) - 3sqrt(2) + 3sqrt(2) - 2sqrt(3))/((3 - 2))` =  `sqrt(3)`



Question 269.

If `sqrt(2)` = 1.414,  the square root of  `(sqrt(2) - 1)/(sqrt(2) + 1)` is nearest  to


  1.    0.172
  2.    0.414
  3.    0.586
  4.    1.414
 Discuss Question
Answer: Option B. -> 0.414

`(sqrt(2) - 1)/(sqrt(2) + 1)` = `(sqrt(2) - 1)/(sqrt(2) + 1)` x `(sqrt(2) - 1)/(sqrt(2) -1)`

= `(sqrt(2) - 1)^2`

`:.` ` sqrt( (sqrt(2) - 1)/(sqrt(2) + 1))` = `(sqrt(2) - 1)` = (1.414 - 1 )=  0.414



Question 270.

if `(5 + 2sqrt(3))/(7 + 4sqrt(3))` =`  a + bsqrt(3)` , them :


  1.    a = - 11, b = - 6
  2.    a = - 11, b = 6
  3.    a = 11, b = - 6
  4.    a = 6, b = 11
 Discuss Question
Answer: Option C. -> a = 11, b = - 6

`a + bsqrt(3)` =  `(5 + 2sqrt(3))/(7 + 4sqrt(3))` x `(7 -  4sqrt(3))/(7 - 4sqrt(3))`

`(35 - 20sqrt(3) + 14sqrt(3) - 24)/((7)^2 - (4sqrt(3))^2)` =  `(11 - 6sqrt(3))/(49 - 48)` =  `11 - 6sqrt(3)`

`:.`  a = 11, b = - 6



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