NCERT Ganita Prakash, Class 8, textbook pages 1–22 (Part 1)

How to teach Class 8 Maths Chapter 1, A Square and a Cube, at home

Squares, square roots, cubes and cube roots, taught with things you already have at home: a 30-minute activity, a game for the week, a 5-day plan and the mistakes to watch for.

4² = 16cube√144 = 12∛125 = 5

NCERT Class 8 Maths Chapter 1 A Square and a Cube: what it teaches

A queen’s puzzle about lockers leads to square numbers. Your child finds squares and square roots, patterns in their last digits, perfect cubes and cube roots, and estimates roots of numbers that aren’t perfect squares.

Why it matters later. Squares and roots are needed for the Pythagoras theorem (Part 2), algebraic identities and Class 9 real numbers.

See it: this chapter in pictures

144 = 2⁴ × 3²√144 = 2² × 3= 12
Take one from each pair.
squares end in0, 1, 4, 5, 6, 9never 2, 3, 7, 8
A quick test for non-squares.
√50between 7 and 8≈ 7.07
Find the squares on either side.

You need

  • square tiles or squared paper
  • small cubes or dice
  • a calculator for checking

Tonight’s 30 minutes

  1. Build squares from tiles: 1, 4, 9, 16. Build cubes from small cubes: 1, 8, 27.
  2. Find √144 by prime factorisation: 144 = 2⁴ × 3², so √144 = 2² × 3 = 12.
  3. Which numbers can’t be perfect squares? (Those ending in 2, 3, 7, 8.)
  4. Estimate √50: between 7 and 8, closer to 7.

Words to use

  • square
  • square root
  • perfect square
  • cube
  • cube root
  • estimate

Watch for

  • Thinking √ of a number is half of it. √16 = 4, not 8: the root times itself gives the number.
  • Pairing prime factors wrongly. Group equal primes in pairs for square roots, triples for cube roots.

What it sounds like at home

A short example of the conversation. Your words will differ; the questions are what matter.

YouIs 64 a square or a cube?

Your childBoth! 8 × 8 and 4 × 4 × 4.

A game for this week: Square or not?

  1. Call a number.
  2. Players say perfect square, perfect cube, both or neither.
  3. Check by factorisation.
  4. Point for each correct call.

A 5-day plan, 30 minutes a day

  1. Day 1Tile squares and cube stacks.
  2. Day 2Square roots by factorisation.
  3. Day 3Last-digit patterns.
  4. Day 4Estimating roots.
  5. Day 5Square or not? game.

Everyday moments to practise

  • Square tiles on floors.
  • Dice and cube boxes.
  • Screen sizes.
  • Area of square plots.

Quick check

Ask these at the end of the week. Tap to see the answer.

√144?

12.

Cube of 5?

125.

Is 2,352 a perfect square?

No; it ends in 2.

Ready for the next chapter when your child…

  • Finds squares and cubes.
  • Finds roots by prime factorisation.
  • Estimates non-perfect roots.

Activities, wording and illustrations are Mathify Kids’ own, following the topics of NCERT’s Ganita Prakash (Class 8). See the full Class 8 parent guide for every chapter.

Questions parents ask

How do I find a square root without a calculator?

Use prime factorisation and take one factor from each pair.

Which number is both a square and a cube?

64 (8² and 4³), and 1 and 729.

How do I estimate √50?

It lies between √49 = 7 and √64 = 8.