Squares and Square Roots Class 8 Maths Worksheet with Quiz and Activities
Work with squares and square roots: spot perfect squares, use the odd number pattern, factorise to find roots and complete Pythagorean triplets. On WitKnowLearn you get the Squares and Square Roots Class 8 online quiz, online activities and interactive games, a square lab, a virtual lab and a worksheet-style practice sheet for Class 8 Maths.
Squares and Square Roots Class 8 Online Quiz
20 questions: 10 easy, 5 average and 5 thinking. Tap an answer and the next question comes up.
Squares and Square Roots Class 8 Activities
👆 Tap a tab to switch: Learn, Games, Labs, Challenges, Virtual Lab and Practice sheet
Squares and Square Roots: Perfect Squares, Roots and Triplets
A short read for Class 8 before you play. These notes cover Squares and Square Roots in a way that suits students of any board.
🔵 What is a square number?
A square number is a number multiplied by itself, such as 5 x 5 = 25. Square numbers end only in 0, 1, 4, 5, 6 or 9, and the squares of even numbers are even while the squares of odd numbers are odd. Between n squared and the next square there are exactly 2n numbers.
🧩 Patterns and Pythagorean triplets
The sum of the first n odd numbers is n squared, because each new odd number adds an L-shaped border to a square of tiles. Three numbers form a Pythagorean triplet when the squares of the two smaller ones add to the square of the largest, like 3, 4, 5 and 5, 12, 13.
√ Finding square roots
The square root undoes squaring. To find the root of a large number, write it as a product of primes, make pairs and take one number from each pair. For a number that is not a perfect square, find the squares on either side to estimate the root.
Squares and Square Roots Class 8 Maths Activities
Follow every step on the Number Train. Earn up to 3 stars in every activity.
This page covers Squares and Square Roots for Class 8 maths and suits students of any board. It covers perfect squares, patterns in squares, Pythagorean triplets and square roots by prime factorisation and estimation.
The activities are pitched at Class 8 level. Sort perfect squares, match roots, use the odd number pattern and grow a square tile by tile in the studio. Explore more Class 8 maths worksheets on WitKnowLearn after this chapter.
Key ideas and facts to know
| Number | Prime factors | Square root |
|---|---|---|
| 144 | 2 x 2 x 2 x 2 x 3 x 3 | 12 |
| 1764 | 2 x 2 x 3 x 3 x 7 x 7 | 42 |
| 72 | 2 x 2 x 2 x 3 x 3 | not perfect |
How to use this page
- Flip the six cards and try the Square Lab in the Learn tab.
- Play the five games and the five labs to practise each idea.
- Finish the five challenges to collect up to 15 points.
- Do two virtual experiments and grow a square from tiles in the studio.
- Take the 20-question online quiz, with assertion and reason and case study questions, and fill in the practice sheet.
Worked examples
1764 = 2 x 2 x 3 x 3 x 7 x 7, so the root is 2 x 3 x 7 = 42.
72 = 2 x 2 x 2 x 3 x 3. Multiply by 2 to get 144.
This Squares and Square Roots worksheet for Class 8 science gives you online activities and interactive games that make the chapter clear. Every activity has a goal, a hint and a short fact, so students learn while they enjoy.
Complete Guide: Class 8 Maths Squares and Square Roots
This guide is for Class 8 students, parents and teachers. It covers Squares and Square Roots for Class 8 maths and shows how to use the quiz, labs and games on this page.
Introduction to Squares and Square Roots
Squares and square roots connect number patterns with area. This topic shows how to recognise perfect squares, find roots by factorising and use triplets to solve right triangles.
What is there in this chapter
- Square numbers and their properties
- Patterns in squares
- Pythagorean triplets
- Square root by prime factorisation
- Estimating square roots
Learning objectives
- Recognise perfect squares.
- Use patterns in squares.
- Find square roots by factorisation.
- Estimate roots of other numbers.
- Reason with assertions and case studies.
Learning outcomes
- I can tell if a number is a perfect square.
- I can find roots by pairing prime factors.
- I can use Pythagorean triplets.
Squares and Square Roots Class 8 resources on this page
| Resource | What it gives |
|---|---|
| Online quiz | 20 questions: 10 easy, 5 average and 5 thinking, with assertion and reason and case study questions and a full review |
| Flip cards | 6 picture cards with one-line rules |
| Square Lab | A hands-on lab with 3 rounds |
| Games | 5 interactive games |
| Labs | 5 activity labs |
| Virtual Lab | 2 experiments plus a studio that grows a square from tiles |
| Challenges | 5 challenges, 15 points in all |
| Practice sheet | A worksheet-style sheet with 16 questions, name and date lines and a live score |
Key facts
| Idea | Rule |
|---|---|
| Perfect square | ends in 0, 1, 4, 5, 6 or 9 |
| Odd number sum | first n odd numbers add to n squared |
| Between squares | 2n numbers |
| Prime factors | come in pairs |
| Triplet | a squared + b squared = c squared |
Types of questions you may see
- Identify perfect squares
- Assertion and reason on factors
- Case study on a square garden
- Triplets and estimation
Solved examples
13 x 13 = 169, so the root is 0.13.
The side is 25 m, so the fence is 4 x 25 = 100 m.
Common mistakes
| Mistake | Correct idea |
|---|---|
| Saying the square root of 16 is 8 | The root of 16 is 4, since 4 x 4 = 16 |
| Saying 50 is a perfect square | 50 is between 49 and 64 |
| Forgetting to take one of each pair | Take one factor from every pair |
Squares and Square Roots in daily life
Squares give the area of floors, tiles, gardens and screens, and square roots help find the side of a square from its area and the length of a diagonal.
Tips for parents and teachers
- Learn the squares up to 20.
- Check the units digit before factorising.
- Practise one assertion and one case study each week.
Related Class 8 Maths Worksheets
Squares and Square Roots Class 8 FAQs
What is a perfect square?
A perfect square is the square of a whole number, such as 49 = 7 x 7. It always ends in 0, 1, 4, 5, 6 or 9.
How do you find a square root by prime factorisation?
Write the number as a product of primes, make pairs of equal factors and multiply one factor from each pair. For 144 the root is 2 x 2 x 3 = 12.
What is the sum of the first n odd numbers?
It is n squared. For example 1 + 3 + 5 + 7 = 16 = 4 squared.
What is a Pythagorean triplet?
It is three numbers where the squares of the two smaller ones add to the square of the largest, such as 3, 4, 5 and 5, 12, 13.
What can students do on this page?
Students can take a 20-question online quiz with assertion and reason and case study questions, play five games, try five online activities, finish five challenges, run the Square Lab, do two virtual experiments, grow a square from tiles in the tile and table views,, and fill in a 16-question practice sheet with a Show answers button.
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