How do I solve Squares and Square Roots problems?

The square of a number n is n². For example, 12² = 144. A perfect square ends in 0, 1, 4, 5, 6, or 9. It never ends in 2, 3, 7, or 8.

What are common mistakes in Squares and Square Roots?

Thinking all numbers ending in 0, 1, 4, 5, 6, 9 are perfect squares (they are necessary but not sufficient). Forgetting that negative numbers do not have real square roots.

Which class covers Squares and Square Roots?

Squares and Square Roots is typically taught in Class 8. SparkEd has free practice for all these grades.

Where can I practise Squares and Square Roots for free?

SparkEd offers free chapter-wise practice for Squares and Square Roots aligned to CBSE, ICSE, and IB curricula. Visit sparkedmaths.com to start.

How to Solve Squares and Square Roots — Step by Step Guide

Finding squares, square roots and properties of perfect squares. This guide covers Class 8 to 8.

Step-by-Step Method

1
The square of a number n is n². For example, 12² = 144.
2
A perfect square ends in 0, 1, 4, 5, 6, or 9. It never ends in 2, 3, 7, or 8.
3
To find the square root by prime factorisation: factorise the number and pair the prime factors.
4
To find square root by division method: group digits in pairs from right to left, then divide step by step.
5
Properties: square of an even number is even, square of an odd number is odd.

Worked Example

Problem: Find the square root of 324 by prime factorisation.

Solution: 324 = 2² × 3⁴ = 2² × (3²)². √324 = 2 × 3² = 2 × 9 = 18.

Common Mistakes to Avoid

✗
Thinking all numbers ending in 0, 1, 4, 5, 6, 9 are perfect squares (they are necessary but not sufficient).
✗
Forgetting that negative numbers do not have real square roots.
✗
Pairing digits from left to right instead of right to left in the long division method.
✗
Not simplifying square roots fully (e.g., √50 = 5√2, not just √50).

Practice Squares and Square Roots on SparkEd

Get free chapter-wise practice questions aligned to your board:

CBSE Class 8 Squares and Square Roots

Master Squares and Square Roots with Free Practice

30,000+ questions, AI solver for instant help, and printable worksheets. 100% free.

Start Practising Free Play Zone (Class 1-5)

Frequently Asked Questions

How do I solve Squares and Square Roots problems?: The square of a number n is n². For example, 12² = 144. A perfect square ends in 0, 1, 4, 5, 6, or 9. It never ends in 2, 3, 7, or 8.
What are common mistakes in Squares and Square Roots?: Thinking all numbers ending in 0, 1, 4, 5, 6, 9 are perfect squares (they are necessary but not sufficient). Forgetting that negative numbers do not have real square roots.
Which class covers Squares and Square Roots?: Squares and Square Roots is typically taught in Class 8. SparkEd has free practice for all these grades.
Where can I practise Squares and Square Roots for free?: SparkEd offers free chapter-wise practice for Squares and Square Roots aligned to CBSE, ICSE, and IB curricula. Visit sparkedmaths.com to start.

SparkEd Maths — sparked.coms@gmail.com — www.sparkedmaths.com