Worksheets › Class 8 › A Square and a Cube: Thinking Puzzles
Class 8 · Computational Thinking and AI worksheetA Square and a Cube: Thinking Puzzles
CBSE Computational Thinking and AI. Squares and cubes by prime factorisation, smallest multipliers, number machines, odd-number and cube-sum patterns, painted cubes. Every sheet has 20 questions in three sections and an answer key, and the questions change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
A perfect square can never end in which digit?
- 4
- 9
- 1
- 7
Answer
(d) 7
squares end in 0, 1, 4, 5, 6 or 9
- 2.
50 × k is a perfect cube. What is the smallest natural number k?
- 40
- 2
- 50
- 20
Answer
(d) 20
50 = 2 × 5²; raise every exponent to a multiple of 3: k = 20, and 50 × 20 = 1,000 = 10³
- 3.
What is the smallest natural number k such that 1,400 ÷ k is a perfect square?
- 16
- 28
- 14
- 100
Answer
(c) 14
1,400 = 2³ × 5² × 7; remove one of each prime with an odd exponent: k = 14, and 1,400 ÷ 14 = 100 = 10²
Section B · short answer
- 4.
Why can 2,000 not be a perfect square? Use its last digits.
Answer
A perfect square ends in an even number of zeros; 2,000 ends in three zeros.
- 5.
Find the cube root of 29,791 using prime factorisation.
Answer
31
29,791 = 31³; take one prime from each group of three: 31 = 31
Section C · long answer
- 6.
A gardener has 195 square tiles and wants to lay the largest possible square with them. (a) How many tiles long is each side? (b) How many tiles are left over? (c) How many more tiles would she need for a square one tile longer on each side?
Answer
(a) 13; (b) 26; (c) 1
13² = 169 ≤ 195 < 196
Fresh sheets for your child
In the app, every A Square and a Cube: Thinking Puzzles sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
Coming soon for Android and iPhone.