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All questions of Square Roots & Cube Roots for DSSSB TGT/PGT/PRT Exam

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Which of the following is a perfect square number?
  • a)
    222222
  • b)
    23453
  • c)
    1681
  • d)
    1057
Correct answer is option 'C'. Can you explain this answer?

Shashwat Singh answered
The answer is 1681 because it is the only number which has it's last digit as a number which a perfect square can have . 9×9=81 the last digit is 1.

Find the perfect square number between 30 and 40.
  • a)
    36
  • b)
    49
  • c)
    25
  • d)
    none of these
Correct answer is option 'A'. Can you explain this answer?

Amita Verma answered
Since, 1 x 1 = 1
         2 x 2 = 4
         3 x 3 = 9
         4 x 4 = 16
         5 x 5 = 25
         6 x 6 = 36
         7 x 7 = 49
 
Thus, 36 is a perfact square number between 30 and 40.

Which of the following would end with digit 1?
  • a)
    1232
  • b)
    1612
  • c)
    772
  • d)
    822
Correct answer is 'B'. Can you explain this answer?

Sneha Singh answered
Option B is correct because the unit digit of 161 is 1 and if unit digit of any digit ends with 1 the its square will also end with 1.

The square of which of the following would be even number?
  • a)
    2826                    
  • b)
    7779              
  • c)
    1057              
  • d)
    131
Correct answer is option 'A'. Can you explain this answer?

Ritu Joshi answered
Since the square of an odd natural number is odd and that of an even number is an even number.
∴    (i)  The square of 431 is an odd number
(∵  431 is an odd number)
(ii)   The square of 2826 is an even nnumber.
(∵ 2826 is an even number)
(iii) The square of 7779 is an odd number
(∵ 7779 is an odd number)
(iv)  The square of 131 is an odd nnumber.
(∵ 82004 is an odd number)

Without adding, find the sum. 1 + 3 + 5 + 7 + 9
  • a)
    16
  • b)
    36
  • c)
    9
  • d)
    25
Correct answer is option 'D'. Can you explain this answer?

Kiran Mehta answered
Here, we have to find the sum of first five odd natural numbers.
Therefore, 1 + 3 + 5 + 7 + 9 = (5)2 = 25

What is the least perfect square which is divisible by each of 21, 36 and 66?
  • a)
    213444
  • b)
    214434
  • c)
    214344
  • d)
    231444
Correct answer is option 'A'. Can you explain this answer?

Ishani Rane answered
L.C.M. of 21, 36, 66 = 2772
Now, 2772 = 2 * 2 * 3 * 3 * 7 * 11
To make it a perfect square, it must be multiplied by 7 x 11.
So, required number = 2 * 2 * 3 * 3 * 7 * 7 * 11 * 11 = 213444

 
  • a)
    13.41
  • b)
    20.46
  • c)
    21.66
  • d)
    22.35
Correct answer is option 'D'. Can you explain this answer?

The Bold answered
3√5 + √125 = (3√5)+(√5×5×5) = (3√5)+(5√5)=8√5 =17.88

√80+6√5=(√5×2×2×2×2) + (6√5)
=4√5 + 6√5
=10√5

we know , √5=2.236
10√5=(10×2.236)=22.36 (approximately)

or

10√5=(8√5+2√5)=17.88+(2×2.236)=17.35(approximately)

so the ans is D.

How many non square numbers lie between 11and 122?
  • a)
    21
  • b)
    23
  • c)
    22
  • d)
     20
Correct answer is option 'C'. Can you explain this answer?

Aditi Saxena answered
11^2 = 11*11 = 
12112^2 = 12*12 = 144
Now numbers are between 121 and 144 are:122, 123, 124,143 Total number = 22

The square root of 16641 is
  • a)
    129
  • b)
    121
  • c)
    211
  • d)
    229
Correct answer is option 'A'. Can you explain this answer?

Nikita Singh answered
Step 1:
  • We now need to obtain the digital root of the number. Here's how you do it:
  • Split the number up and add each digit together:
    1 + 6 + 6 + 4 + 1 = 18
  • If the answer is more than one digit, you would add each digit of the answer together again:
    1 + 8 = 9
  • What is the digital root of number 16,641?
    Answer: 9
Step 2:
  • So now we know the digital root of 16,641 is 9. Is 9 in the list of digital roots that are always a square root (1, 4, 7 or 9)?
  • Answer: YES, 9 is in the list of digital roots that are always perfect squares. We can conclude that 16,641 could be a perfect square!
Factoring
  • OK, so now we know that 16,641 could be a perfect square. We have to find the factors of the number to be sure.
  • Here are all of the factors of 16,641:
    (1 x 16,641) (3 x 5,547) (9 x 1,849) (43 x 387) (129 x 129)
Hence the answer is 129.
 

By which smallest number 48 must be divided so as to make it a perfect square ?
  • a)
    2
  • b)
    3
  • c)
    6
  • d)
    4
Correct answer is option 'B'. Can you explain this answer?

Anita Menon answered
By Prime factorisation, we have 48=2*2*2*2*3. We have two pairs of 2 but no pair of 3. Hence 48 must be divided by 3 to make it a perfect square.

Can you explain the answer of this question below:

  • A:

  • B:

    7/36

  • C:

    36/7

  • D:

The answer is c.

Meera Rana answered
► Using identity, (a-b)2 = a2 + b2 - 2ab
► Here a = √7 and b = 1/√7
 
= (√7)+ (1/√7)2 - 2. √7.1/√7
= 7 + 1/7 - 2
= 5 + 1/7
= 36/7

The least perfect square, which is divisible by each of 21, 36 and 66 is:
  • a)
    213444
  • b)
    214344
  • c)
    214434
  • d)
    231444
Correct answer is option 'A'. Can you explain this answer?

Ishani Rane answered
L.C.M of 21,36,66=2772
Now, 2772=2*2*3*3*7*11
Hence to make it a perfect square , it must be multiplied by 7*11
∴ The required number is 2^2*3^3*7^2*11^2 
= 213444

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