Mathematics Class 8 - Squares And-Square-Roots Notes

Squares and Square Roots

Welcome to the chapter on Squares and Square Roots for Class 8. In this chapter, you will learn what squares and square roots are, how to find them, and how to use them in solving problems. By the end of this chapter, you will be able to calculate squares and square roots and solve related word problems confidently!

Introduction

Squares and square roots are important concepts in mathematics. A square is the product of a number multiplied by itself. The square root is the number that, when multiplied by itself, gives the original number.

Squares

The square of a number is found by multiplying the number by itself.

• Example: The square of 5 is 5 × 5 = 25
• Example: The square of 12 is 12 × 12 = 144

Squares are always positive numbers.

Properties of Squares

• The square of any integer is always non-negative.
• The last digit of a perfect square can only be 0, 1, 4, 5, 6, or 9.
• The square of an even number is even; the square of an odd number is odd.

Square Roots

The square root of a number is the value that, when multiplied by itself, gives the original number.

• Example: The square root of 25 is 5, because 5 × 5 = 25
• Example: The square root of 144 is 12, because 12 × 12 = 144

The symbol for square root is √.

Finding Square Roots

• By prime factorization
• By division method
• By using tables of squares

Perfect Squares and Non-Perfect Squares

• A perfect square is a number that is the square of an integer (e.g., 1, 4, 9, 16, 25).
• Non-perfect squares do not have whole number square roots (e.g., 2, 3, 5, 7).

Word Problems

Use squares and square roots to solve real-life problems. Read the question, identify what is asked, and use the correct operation.

• Example: If the area of a square is 49 cm², what is the length of one side? (√49 = 7 cm)

Fun Activity: Square Root Hunt!

Write down the squares of numbers from 1 to 20. Find their square roots and see which numbers are perfect squares!

Summary

• A square is the product of a number multiplied by itself.
• A square root is the number that gives the original number when multiplied by itself.
• Use squares and square roots to solve math problems and word problems.

Practice Questions

1. Find the square of 15.
2. What is the square root of 81?
3. Is 50 a perfect square?
4. Find the square root of 225.
5. If the side of a square is 9 cm, what is its area?

Challenge Yourself

• List all perfect squares between 1 and 100.
• Find the square root of 400 using prime factorization.

Did You Know?

• The square root of 2 is an irrational number and cannot be written exactly as a fraction!
• Squares and square roots are used in geometry, algebra, and even in science!

Glossary

• Square: The product of a number multiplied by itself.
• Square Root: The number that gives the original number when multiplied by itself.
• Perfect Square: A number that is the square of an integer.
• Irrational Number: A number that cannot be written as a simple fraction.

Answers to Practice Questions

1. 225
2. 9
3. No, because 50 is not the square of any integer.
4. 15
5. 81 cm²

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Practice squares and square roots to become confident in math!