RS Aggarwal Class 8 Mathematics Solutions for Chapter-3 Squares and Square Roots

Definitions of Squares and Square Roots

The Square of a number is the value generated by multiplying the number by itself.

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

For example:

(6)² = 36

The Square of 6 is 36 whereas 6 is the square root of 36. Therefore, the concept of the square and square root are opposite.

Properties of Square Number

• The Square of any number gives a positive number.

• The Square of 1 is 1.

• The Square of 0 is 0.

• The Square of a number under the root gives the same number as the number under the root.

• For example (√3)² = 3

There are 2 ways to find the square root of a number accurately:

• Prime Factorisation Method

• Using Long Division Method

The easier of the two methods is the Prime Factorisation Method.

It can be explained with the help of an example:

Question: Find the square root of 150.

First, we need to find the factors of 150

150 = 2 × 3 × 5 × 5

Now, putting both sides under square root we get;

√150=2×3×5×5

Since 5 occur 2 times, 5 come outside the root.

Therefore,

√150=5√6

Squares and Square Roots of Numbers From 1 to 50

Perfect and Imperfect Square

Perfect Square: The square root of an ant number is perfect if a whole number is multiplied by itself to generate a given number.

Imperfect Square: Square root of a number is imperfect if a whole number is not multiplied to generate a given number.

How to Find in Between Squares?

Suppose the 2 consecutive squares are n² and (n+1)², then the number between them is 2n.

For example:

Find the numbers between 2² and 3².

2² = 4

3² = 9

And, n = 2

Therefore, the total numbers between 4 and 9 = 2n = 4

Therefore, the numbers are 5, 6, 7, 8.

What is the Pythagorean Triplet?

3 positive integers a, b, c which satisfies this Pythagoras theorem a²+b²=c² is called the Pythagorean Triplet and the positive integers are called Pythagorean triples.

Example: (3, 4, 5)

By evaluating we get:

32 + 42 = 52

9 + 16 = 25

Hence, 3, 4, and 5 are the Pythagorean triples.

Preparation Tips

1. First, go through the chapter thoroughly and cover all the topics.

2. Note down all the important formulae and try to learn them.

3. Start solving the exercise questions without any guidance from anyone.

4. Try the questions at least 3 times if you are unable to solve them.

5. Seek help from Vedantu’s solution to check your answers and solve the ones that you were unable to solve.

Key benefits of using the RS Aggarwal Class 8 Mathematics Solutions for Chapter-3 Squares and Square Roots via Vedantu:

The following are the key benefits of using the RS Aggarwal Class 8 Mathematics Solutions for Chapter-3 Squares and Square Roots via Vedantu:

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Learn how to attempt the problems in the exercise of chapter 3 Squares and Square Roots by downloading this solution PDF file from Vedantu. Keep it handy and clear your doubts whenever you need it while practicing and solving the problems of these exercises.