Square Root and Cube Root - Aptitude Questions and Answers

Square Root and Cube Root Questions and Answers

Learn and practice the chapter "Square Root and Cube Root" with these solved Aptitude Questions and Answers. Each question in the topic is accompanied by a clear and easy explanation, diagrams, formulae, shortcuts and tricks that help in understanding the concept.

Use of Square Root and Cube Root Questions

The questions and examples given in this section will be useful to all the freshers, college students and engineering students preparing for placement tests or any competitive exam like MBA, CAT, MAT, SNAP, MHCET, XAT, NMAT, GATE, Bank exams - IBPS, SBI, RBI, RRB, SSB, SSC, UPSC etc.

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1. Rajesh was shifting his shop. When he tried to pack 85 similar cartons in each bag, he realised that he could not completely fill 9 bags. However, when he reduced the number of cartons in each bag to 58, 13 bags got insufficient. However, at the end he could pack all the cartons by packing X carton in X bags. How many total cartons did he have?

a. 729
b. 765
c. 784
d. 812

Answer: c. 784

Explanation:

Since X bags are there and each has X cartons, Total cartons = X * X = X2
Only options C and D are perfect squares.
729 is a perfect square
But it cannot be answer as condition is that with 58 books in each bag, 13 bags are not sufficient.
58 x 13 = 754 > 729
So if 729 is the answer, 13 bags are sufficient.
So answer is Option D = 784


2. Prashant had some pebbles in his treasure. His friend said, that he could arrange all the 17424 pebbles in a two dimensional square matrix. How many rows did he make?

a. 132
b. 138
c. 141.2
d. 145.8

Answer: b. 138

Explanation:

Since it is a square matrix, no. of rows = No. of columns
Let number of pebbles in each row be P
∴ Number of rows = P
Total Pebbles = P x P = P2 = 17424
∴ P = 132 = No. of rows

Tip:
To find square root of numbers -
17424  = Last digit i.e. digit in unit's place is 4
So square root will have 2 or 8 at the end.
Now leave last 2 digits. We are left with 174.
Nearest square to 174 which is less than 174 is 169.
169 is square of 13
So the square root is 132 or 138.
Now add 13 to 169
∴ 169 + 13 = 182
174<182 so answer is 132 = smaller number
Note - If after addition, 174> addition,
Then answer would be the greater number i.e. 138


3. Find the least number with which you would divide 384, to get a perfect square.

a. 2
b. 3
c. 6
d. 8

Answer: c. 6

Explanation:

Here, first we must find factors of 384 by simple division
----------------------
2              384
----------------------
2              192
2              96
2              48
2              24
2              12
2              6
3              3
                1
----------------------
Factors of 384 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 = 22 x 22 x 22 x 2 x 3
Here we can see that all factors are in form of squares except two factors
If we divide by extra 2 and extra 3, it will be 22 x 22 x 22 = 22 x 22 x 22   
Since all factors are in form of squares, the number too will be a perfect square.
So we need to divide 384 by (2 x 3 =) 6 to get perfect square.


4. X = (Perfect square number nearest to 1500) - (1500)
Find X.


a. 5
b. 56
c. 100
d. 131
e. None of the above

Answer: e. None of the above

Explanation:

In such scenarios, trial and error method is suitable
We know that 402 = 1600
So we must start finding squares of numbers less than 40
Take 39 first
How to find 392?

Finding the square of 2 digit numbers
Example 392
Find nearest multiple of 10 from 39. Here it is 40
40 - 39 = 1
Now subtract this value i.e. 1 from 39
∴ 39 - 1 = 38
Now multiply 40 and 38
∴ 40 x 38 = 40(30 + 8) = 1200 + 320 = 1520
The value we found by subtraction earlier is 1
Add 12 to 1520
∴ 392 = 1520 + 12 = 1521


402 = 1600      1600 - 1500 = 100
392 = 1521      ∴ 1521 - 1500 = 21
382 = 1444      ∴ 1500 - 1444 = 56
Thus nearest perfect square is 392. But there is no option of difference of 21.
So answer is None of the above


5. X = (- 21952)1/3 . Find X.

a. -38
b. -34
c. -28
d. -27

Answer: c. -28

Explanation:

(-21952)1/3 = ((-1)(21952))1/3 = (-1)1/3 x (21952)1/3 = - (21952)1/3

Finding cube root of any number easily
(21952)1/3 = Last digit i.e. digit in unit's place is 2
Cube of 8 has 2 in unit's place.
So cube root will have 8 at the end.
Now leave last 3 digits. We are left with 21.
Nearest cube to 21 which is less than 21 is 8.
8 is cube of 2. (Cube of 3 is 27 and 27>21)
So cube root is 28.


∴ (-21952)1/3 = -28