Question 1
Powers and roots — instant recall.
15² = ?
- 225
- 240
- 196
- 256
- 210
Show the worked solution
- Use (a − b)²: (20 − 5)² = 400 − 200 + 25 = 225.
Square root and cube root questions with answers
Square root and cube root questions are decided in the exam by recognition, not by extraction. Knowing the squares to 30 and the cubes to 20 turns most of these into a two-second look at the last digit and a range check. Every walkthrough below shows that route rather than the long-division method nobody has time to run.
Download the PDF — 15 questions with answers
Free, ungated, no email. This is the square root and cube root questions with answers PDF — the same 15 questions as below, with every worked solution at the back, ready to print.
How to use this set
The 15 questions below are ordered the way an exam block is rather than easiest-first: two gentle openers, then a run of medium, and a hard one every sixth question — 2 of the 15 sit in the hard band. Every question is a squares, cubes & roots.
Work each question on paper before you open its solution. The walkthrough is the method itself, step for step, so reading it first turns a practice set into a reading exercise and teaches nothing. If you are stuck on the method rather than on one question, the method guide is a better place to start than the next question: Roots by last digit and range.
15 square root and cube root questions with answers
Every question below was generated by the same engine that mints the ComputePrep daily timed drill, and machine-checked before it reached this page — a multiple-choice question validates its own answer against its own options at generation, and ships only with a walkthrough attached. The walkthrough is the engine's own.
Question 2
Powers and roots — instant recall.
20² = ?
- 441
- 361
- 400
- 420
- 380
Show the worked solution
- 20² = 400.
Question 3
Powers and roots — instant recall.
8³ = ?
- 492
- 729
- 343
- 512
- 576
Show the worked solution
- 8³ = 8² × 8 = 64 × 8 = 512. (Exam-standard cube — worth memorising to 15³.)
Question 4
Powers and roots — instant recall.
26² = ?
- 729
- 702
- 679
- 686
- 676
Show the worked solution
- Use (a − b)²: (30 − 4)² = 900 − 240 + 16 = 676.
Question 5
Powers and roots — instant recall.
√900 = ?
- 30
- 29
- 31
- 50
- 28
Show the worked solution
- 30² = 900, so √900 = 30. Anchor on the last digit and the nearest square of a multiple of 10.
Question 6
Powers and roots — instant recall.
50² = ?
- 2486
- 2500
- 2601
- 2450
- 2401
Show the worked solution
- 50² = 2500.
Question 7
Powers and roots — instant recall.
11² = ?
- 131
- 144
- 133
- 121
- 132
Show the worked solution
- Use (a + b)²: (10 + 1)² = 100 + 20 + 1 = 121.
Question 8
Powers and roots — instant recall.
√225 = ?
- 13
- 17
- 16
- 14
- 15
Show the worked solution
- 15² = 225, so √225 = 15. Anchor on the last digit and the nearest square of a multiple of 10.
Question 9
Powers and roots — instant recall.
21² = ?
- 481
- 484
- 400
- 420
- 441
Show the worked solution
- Use (a + b)²: (20 + 1)² = 400 + 40 + 1 = 441.
Question 10
Powers and roots — instant recall.
6³ = ?
- 216
- 125
- 226
- 343
- 252
Show the worked solution
- 6³ = 6² × 6 = 36 × 6 = 216. (Exam-standard cube — worth memorising to 15³.)
Question 11
Powers and roots — instant recall.
23² = ?
- 484
- 529
- 576
- 479
- 506
Show the worked solution
- Use (a + b)²: (20 + 3)² = 400 + 120 + 9 = 529.
Question 12
Powers and roots — instant recall.
∛1331 = ?
- 10
- 31
- 11
- 9
- 12
Show the worked solution
- 11³ = 1331, so ∛1331 = 11. The last digit of a cube pins the root's last digit uniquely.
Question 13
Powers and roots — instant recall.
12² = ?
- 154
- 169
- 144
- 156
- 121
Show the worked solution
- Use (a + b)²: (10 + 2)² = 100 + 40 + 4 = 144.
Question 14
Powers and roots — instant recall.
17² = ?
- 299
- 256
- 289
- 324
- 306
Show the worked solution
- Use (a − b)²: (20 − 3)² = 400 − 120 + 9 = 289.
Question 15
Powers and roots — instant recall.
√625 = ?
- 23
- 26
- 75
- 24
- 25
Show the worked solution
- 25² = 625, so √625 = 25. Anchor on the last digit and the nearest square of a multiple of 10.
Where these questions come from
Most free practice for this topic is a scanned upload or a blog quiz, and neither can tell you a question has exactly one answer. That is the one thing this set can promise: it is minted, not typed. The engine behind it serves ComputePrep's daily timed drill, so the questions here are the same shape as the ones a live round would give you — and there is an unlimited supply of them, which is why this page can be regenerated rather than padded.
If you want the method rather than more questions, Roots by last digit and range covers the approach, the traps and a worked table. This page and that one deliberately answer different questions: that one is how do I solve these, this one is give me square root and cube root questions with the answers.
FAQ
How do I find a cube root by inspection?
The last digit of a cube determines the last digit of its root uniquely: 1→1, 8→2, 7→3, 4→4, 5→5, 6→6, 3→7, 2→8, 9→9, 0→0. Strip the last three digits, find the largest cube below what remains for the leading digit, and the two digits are the answer.
Which squares are worth memorising?
One to thirty, plus the round hundreds. That table alone resolves most exam roots at a glance and speeds up simplification, mensuration and quadratic questions as a side effect. It is the highest-return memorisation in the whole quantitative section.
What if a number is not a perfect square?
Bracket it between the two nearest perfect squares and read the options. Exam sets are built so that only one option falls in the correct range, so approximation almost always beats extraction — and it takes a fraction of the time.
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