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CBSE · Class 8 · Mathematics

A Square and A Cube

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
√784 equals:
  1. 29
  2. 28
  3. 26
  4. 392
2.
113 equals:
  1. 1331
  2. 121
  3. 33
  4. 1342
3.
A number that is the square of a whole number is called a:
  1. perfect cube
  2. prime number
  3. perfect square
  4. triangular number
4.
∛12167 equals:
  1. 4055
  2. 24
  3. 529
  4. 23
5.
Which of these is a perfect cube?
  1. 366
  2. 361
  3. 343
  4. 304
6.
What is the ones digit of 443?
  1. 3
  2. 4
  3. 5
  4. 9
7.
√144 equals:
  1. 11
  2. 14
  3. 12
  4. 72
8.
How many non-square numbers lie between 529 and 576?
  1. 23
  2. 47
  3. 46
  4. 45
Section B — Short answer8 × 2 = 16 marks
9.
Find √64 using prime factorisation.
10.
Find ∛1728 using prime factorisation.
11.
Find the smallest number by which 486 must be multiplied to make a perfect square, and the square root of the result.
12.
Find the smallest number by which 72 must be multiplied to make a perfect cube.
13.
Between which two consecutive whole numbers does √8186 lie?
14.
Write 43 as the sum of 4 consecutive odd numbers.
15.
Find 1452 quickly, using the pattern for numbers ending in 5.
16.
Is 1857 a perfect square? Give a reason.
Section C — Word problems4 × 4 = 16 marks
17.
A square garden has an area of 3844 m2. How long is each side, and how much fencing goes all round it?
18.
A cube-shaped water tank holds 8000 litres, and 1 litre fills a cube of side 10 cm. How long is each side of the tank, in cm?
19.
How many cubes of side 3 cm can be packed into a cube-shaped box of side 24 cm?
20.
9000 is the sum of two perfect cubes. Find them. (Hint: try cubes up to 203.)
AmbifulWorksheets
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CBSE · Class 8 · Mathematics

Answer key

A Square and A Cube · AW-8M-SQR-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(b) 2828 × 28 = 784
2(a) 133111 × 11 × 11
3(c) perfect square—
4(d) 2323 × 23 × 23 = 12167
5(c) 34373 = 343
6(b) 4only the ones digit 4 matters: 43 = 64
7(c) 12—
8(c) 462 × 23
9864 = 26; halve each power: 23 = 8
10121728 = 26 × 33; divide each power by 3: 22 × 3 = 12
116; √2916 = 54486 = 2 × 35: make every power even
12372 = 23 × 32: make every power a multiple of 3 → × 3 = 216 = 63
1390 and 91902 = 8100 < 8186 < 8281 = 912
1413 + 15 + 17 + 19 = 64start at 42 − 4 + 1 = 13
152102514 × 15 = 210, then write 25: 21025
16No432 = 1849 and 442 = 1936; 1857 is between them
1762 m; 248 m√3844 = 62; 4 × 62
18200 cm∛8000 = 20 small cubes along each edge; 20 × 10 cm
1951224 ÷ 3 = 8 along each edge; 83 = 512
20103 + 203 = 1000 + 80001000 + 8000 = 9000