NCERT Class 8 Mathematics Solutions: Chapter 6 – Squares and Square Roots Exercise 6.1 Part 3

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Image of Square Pattern for Squares and Square Roots

Image of Square Pattern for Squares and Square Roots

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Question: 5 Observe the following pattern and supply the missing numbers:

Answer:

Start with 1 followed by a zero.

Then, go up to as many numbers as there are number of 1s given.

Follow the same pattern in reverse order.

= 1020304030201

Question: 6 Using the given pattern, find the missing numbers:

Answer:

Third number is the product of first and second number.

Fourth number is 1 more than third number.

(Here,

(Here,

(Here,

Question 7: Without adding, find the sum:

(i)

(ii)

(iii)

Answer:

(i)

Here, there are first five odd numbers. Therefore square of 5 is 25.

(ii)

Here, there are first ten odd numbers. Therefore square of 10 is 100.

(iii)

Here, there are first twelve odd numbers. Therefore square of 12 is 144.

Question 8:

(i) Express 49 as the sum of 7 odd numbers.

(ii) Express 121 as the sum of 11 odd numbers.

Answer:

(i) 49 is the square of 7. Therefore it is the sum of first 7 odd numbers.

(ii) 121 is the square of 11. Therefore it is the sum of first 11 odd numbers.

Question 9: How many numbers lie between squares of the following numbers?

(i) 12 and 13

(ii) 25 and 26

(iii) 99 and 100

Answer:

(i) 12 and 13

Since, non-perfect square numbers between and are 2n.

Here,

So, non-perfect square numbers between 12 and

Or

Here, , 169 Now,

So, there are numbers lying between and .

(ii) 25 and 26

Since, non-perfect square numbers between and are 2n.

Here,

So, non-perfect square numbers between 25 and

(iii) 99 and 100

Since, non-perfect square numbers between and are 2n.

Here,

So, non-perfect square numbers between 99 and