Square Roots & Cube Roots Quiz: Quantitative Aptitude Practice
10 timed square root and cube root questions for SSC CHSL and other exams. Perfect squares and cubes, decimals, nested roots and surds.
Square Roots & Cube Roots Quiz: Quantitative Aptitude Practice
Tip: use keys 1-4 to answer, Enter for next.
Answers to the starter quiz
Spoilers! These are the Starter quiz’s answers. Easy, Medium, Hard and Mixed rounds show their own answers when you finish.
What is the square root of 5,329?
- 77
- 63
- 83
- 73
Answer: 73. Ends in 9, so the root ends in 3 or 7. 53 lies between 7² = 49 and 8² = 64, so the tens digit is 7; 53 < 7 × 8 = 56, so take 73.
What is the cube root of 12,167?
- 27
- 23
- 33
- 17
Answer: 23. A cube ending in 7 has a root ending in 3. The remaining 12 lies between 2³ = 8 and 3³ = 27, so the root is 23.
What is the smallest number by which 2,592 must be multiplied to make it a perfect square?
- 3
- 2
- 6
- 8
Answer: 2. 2,592 = 2^5 × 3^4. Only 2 has an odd power, so multiplying by 2 gives 2^6 × 3^4 = 72².
What is the square root of 0.0169?
- 0.013
- 1.3
- 0.0013
- 0.13
Answer: 0.13. 169 = 13², and four decimal places become two: sqrt 0.0169 = 0.13.
What is the value of sqrt(12 + sqrt(12 + sqrt(12 + ...))) (continuing endlessly)?
- 4
- 3
- 6
- 12
Answer: 4. Let x be the value. Then x² = 12 + x, so x² - x - 12 = 0, giving x = 4 (the root must be positive).
What is the least number that must be subtracted from 7,850 to make it a perfect square?
- 71
- 96
- 106
- 116
Answer: 106. 88² = 7,744 and 89² = 7,921. The largest square not above 7,850 is 7,744, so subtract 106.
By what least number must 3,087 be divided to make the quotient a perfect cube?
- 3
- 7
- 21
- 9
Answer: 9. 3,087 = 3² × 7³. Remove the 3² to leave 7³ = 343, so divide by 9.
Given sqrt 2 = 1.414, what is the value of sqrt 50 + sqrt 18?
- 11.312
- 10.606
- 9.899
- 12.728
Answer: 11.312. sqrt 50 = 5 sqrt 2 and sqrt 18 = 3 sqrt 2, so the sum is 8 sqrt 2 = 8 × 1.414 = 11.312.
Which of the following is equal to 1/(sqrt 3 - sqrt 2)?
- sqrt 3 - sqrt 2
- (sqrt 3 + sqrt 2)/5
- sqrt 3 + sqrt 2
- 1/sqrt 5
Answer: sqrt 3 + sqrt 2. Multiply top and bottom by sqrt 3 + sqrt 2: the denominator becomes 3 - 2 = 1, leaving sqrt 3 + sqrt 2.
Which of the following cannot be a perfect square?
- 87,423
- 61,504
- 42,849
- 97,344
Answer: 87,423. No perfect square ends in 3 (or 2, 7, 8). The others are squares: 248², 207² and 312².
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