Q 1 Mathematics Square Roots And Cube Roots
Evaluate sqrt(6084) by factorization method?
View answer & explanation Ans: 78
Correct Answer: 78
78 x 78 = 6084, so the square root of 6084 is 78.
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Arithmetic: Square Roots and Cube Roots — Solved MCQs Solved MCQs
Solved square roots and cube roots MCQs — 30 questions on square roots, cube roots, perfect squares and cubes, and least and greatest square and cube problems, with verified answers and explanations. Free online practice for FPSC, PPSC, NTS and all one-paper exams. Covers square roots and cube roots.
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30
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About this paper
This is the Arithmetic: Square Roots and Cube Roots solved MCQ bank from Advanced FPSC & Other Federal Model Papers (Edition 32): 30 published questions (book pp. 780-782, all 30 printed) on evaluating square and cube roots, least and greatest perfect squares and cubes, and numbers to add, subtract, multiply or divide to reach a perfect square or cube. Every answer was re-solved from scratch against the printed Answer Key, and every question carries a worked explanation.
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Arithmetic: Square Roots and Cube Roots — Solved MCQs
Read mode 30 MCQs · 30 minutes
Subject 1
Mathematics
1
Topic Section
Square Roots And Cube Roots
30 solved MCQs shown directly below
Q 2 Mathematics Square Roots And Cube Roots
Find the square root of 1471369:
View answer & explanation Ans: 1213
Correct Answer: 1213
1213 x 1213 = 1471369, so the square root is 1213.
Q 3 Mathematics Square Roots And Cube Roots
Find the value of sqrt(1 9/16):
View answer & explanation Ans: 1 1/4
Correct Answer: 1 1/4
1 9/16 = 25/16, and sqrt(25/16) = 5/4 = 1 1/4.
Q 4 Mathematics Square Roots And Cube Roots
What is the square root of 0.0009?
View answer & explanation Ans: 0.03
Correct Answer: 0.03
0.03 x 0.03 = 0.0009, so the square root is 0.03.
Q 5 Mathematics Square Roots And Cube Roots
Find the value of sqrt(0.289/0.00121):
View answer & explanation Ans: 170/11
Correct Answer: 170/11
sqrt(0.289/0.00121) = sqrt(28900/121) = 170/11, as in solved example (3).
Q 6 Mathematics Square Roots And Cube Roots
Find the least square number which is exactly divisible by 10, 12, 15 and 18:
View answer & explanation Ans: 900
Correct Answer: 900
The LCM of 10, 12, 15 and 18 is 180, and the smallest multiple of 180 that is a perfect square is 180 x 5 = 900 = 30^2.
Q 7 Mathematics Square Roots And Cube Roots
Find the greatest number of five digits which is a perfect square?
View answer & explanation Ans: 99856
Correct Answer: 99856
316^2 = 99856 and 317^2 = 100489 (six digits), so 99856 is the greatest five-digit perfect square.
Q 8 Mathematics Square Roots And Cube Roots
Find the smallest number that must be added to 1780 to make it a perfect square:
View answer & explanation Ans: 69
Correct Answer: 69
The next square above 1780 is 43^2 = 1849, and 1849 - 1780 = 69.
Q 9 Mathematics Square Roots And Cube Roots
Find the cube root of 2744:
View answer & explanation Ans: 14
Correct Answer: 14
14 x 14 x 14 = 2744, so the cube root is 14.
Q 10 Mathematics Square Roots And Cube Roots
By what least number 4320 be multiplied to obtain a number which is a perfect cube?
View answer & explanation Ans: 50
Correct Answer: 50
4320 = 2^5 x 3^3 x 5, so multiplying by 2 x 5^2 = 50 completes every exponent to a multiple of 3.
Q 11 Mathematics Square Roots And Cube Roots
The square root of 64009 is:
View answer & explanation Ans: 253
Correct Answer: 253
253 x 253 = 64009, so the square root is 253.
Q 12 Mathematics Square Roots And Cube Roots
The square root of (272^2 - 128^2) is:
View answer & explanation Ans: 240
Correct Answer: 240
272^2 - 128^2 = (272 - 128)(272 + 128) = 144 x 400 = 57600, whose square root is 240.
Q 13 Mathematics Square Roots And Cube Roots
The digit in the units place in the square root of 15876 is:
View answer & explanation Ans: 6
Correct Answer: 6
sqrt(15876) = 126, so the units digit of the root is 6.
Q 14 Mathematics Square Roots And Cube Roots
What is the square root of 0.16?
View answer & explanation Ans: 0.4
Correct Answer: 0.4
0.4 x 0.4 = 0.16, so the square root is 0.4.
Q 15 Mathematics Square Roots And Cube Roots
sqrt(50) x sqrt(98) is equal to:
View answer & explanation Ans: 70
Correct Answer: 70
sqrt(50) x sqrt(98) = sqrt(4900) = 70.
Q 16 Mathematics Square Roots And Cube Roots
Which one of the following numbers has rational square root?
View answer & explanation Ans: 0.09
Correct Answer: 0.09
The keyed answer is 0.09, whose square root is 0.3. Note the printed item also admits 9, whose square root is 3, so as worded it has two correct options; the keyed answer is retained here.
Q 17 Mathematics Square Roots And Cube Roots
The least perfect square, which is divisible by each of 21, 36 and 66 is:
View answer & explanation Ans: 213444
Correct Answer: 213444
The LCM of 21, 36 and 66 is 2772, and the smallest multiple of 2772 that is a perfect square is 2772 x 77 = 213444 = 462^2.
Q 18 Mathematics Square Roots And Cube Roots
The least perfect square number divisible by 3, 4, 5, 6 and 8 is:
View answer & explanation Ans: 3600
Correct Answer: 3600
The LCM of 3, 4, 5, 6 and 8 is 120, and the smallest multiple of 120 that is a perfect square is 3600 = 60^2.
Q 19 Mathematics Square Roots And Cube Roots
The least number by which 294 must be multiplied to make it perfect square, is:
View answer & explanation Ans: 6
Correct Answer: 6
294 = 2 x 3 x 7^2, so multiplying by 2 x 3 = 6 gives 42^2.
Q 20 Mathematics Square Roots And Cube Roots
Find the smallest number by which 5808 should be multiplied so that the product becomes a perfect square:
View answer & explanation Ans: 3
Correct Answer: 3
5808 = 2^4 x 3 x 11^2, so multiplying by 3 completes the square to 132^2.
Q 21 Mathematics Square Roots And Cube Roots
The least number by which 1470 must be divided to get a number which is a perfect square is:
View answer & explanation Ans: 30
Correct Answer: 30
1470 = 2 x 3 x 5 x 7^2, so dividing by 2 x 3 x 5 = 30 leaves 49 = 7^2.
Q 22 Mathematics Square Roots And Cube Roots
What is the smallest number to be subtracted from 549162 in order to make it a perfect square:
View answer & explanation Ans: 81
Correct Answer: 81
741^2 = 549081, and 549162 - 549081 = 81.
Q 23 Mathematics Square Roots And Cube Roots
The smallest number added to 680621 to make the sum a perfect square is:
View answer & explanation Ans: 4
Correct Answer: 4
The next square above 680621 is 825^2 = 680625, and 680625 - 680621 = 4.
Q 24 Mathematics Square Roots And Cube Roots
The greatest four digit perfect square number is:
View answer & explanation Ans: 9801
Correct Answer: 9801
99^2 = 9801 and 100^2 = 10000 (five digits), so 9801 is the greatest four-digit perfect square.
Q 25 Mathematics Square Roots And Cube Roots
The least number of 4 digit which is perfect square, is:
View answer & explanation Ans: 1024
Correct Answer: 1024
32^2 = 1024, and 31^2 = 961 has only three digits, so 1024 is the least four-digit perfect square.
Q 26 Mathematics Square Roots And Cube Roots
A man plants 15376 apple trees in his garden and arranges them so that there are as many rows as there are apple trees in each row. The number of rows is:
View answer & explanation Ans: 124
Correct Answer: 124
Equal rows and trees per row means rows^2 = 15376, and 124^2 = 15376, so there are 124 rows.
Q 27 Mathematics Square Roots And Cube Roots
The cube root of .000216 is:
View answer & explanation Ans: .06
Correct Answer: .06
0.06 x 0.06 x 0.06 = 0.000216, so the cube root is 0.06.
Q 28 Mathematics Square Roots And Cube Roots
The largest four digit number which is a perfect cube is:
View answer & explanation Ans: 9261
Correct Answer: 9261
21^3 = 9261 and 22^3 = 10648 (five digits), so 9261 is the largest four-digit perfect cube.
Q 29 Mathematics Square Roots And Cube Roots
By what least number 675 be multiplied to obtain a number which is a perfect cube?
View answer & explanation Ans: 5
Correct Answer: 5
675 = 3^3 x 5^2, so multiplying by 5 completes the cube to 15^3.
Q 30 Mathematics Square Roots And Cube Roots
What is the smallest number by which 3600 be divided to make it a perfect cube?
View answer & explanation Ans: 450
Correct Answer: 450
3600 = 2^4 x 3^2 x 5^2, so dividing by 2 x 3^2 x 5^2 = 450 leaves 8 = 2^3.
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Paper practice FAQs
How many questions are in the Arithmetic: Square Roots and Cube Roots MCQ bank? +
30 questions, all 30 printed in the book. No item was dropped: every keyed answer was verified by re-solving.
What does the Square Roots and Cube Roots bank cover? +
Evaluating square roots such as sqrt(6084) and sqrt(1471369), cube roots such as the cube root of 2744, the greatest and least four- and five-digit perfect squares, and the smallest number to add, subtract, multiply or divide to make a perfect square or a perfect cube.
Are the answers verified? +
Yes. Every published answer was re-solved from scratch and checked against the book's printed Answer Key on p. 782; all 30 published answers agree with the key. One item carries a reading note rather than an override: Q16's keyed answer is 0.09 (square root 0.3), but option (d) 9 also has a rational square root (3), so the printed item as worded admits two correct options — that is stated in the question's explanation.
Which other exams does this bank help with? +
Square root and cube root questions of this form appear in FPSC, PPSC, NTS, OTS and other one-paper exams, as well as CSS MPT-style quantitative sections, so the bank is tagged for all of them.