NCERT Solutions Class 8 Maths Chapter 5 Squares and Square Root Exercise 5.1

Exercise 5.1 of Class 8 Maths Chapter 5 teaches students to understand the fundamental meaning of squares of numbers. In this exercise, you will study how to obtain squares of natural numbers, identify square numbers, and apply various patterns to obtain answers. These subjects are important for your examinations, and all higher classes as well.

The NCERT Solutions are up-to-date and aligned to the latest NCERT syllabus, and follow the structure prescribed in the prescribed NCERT textbook. A regular practice of this exercise will increase the speed and accuracy of your answers, and will assist in developing your mental calculations and logical reasoning.

This exercise can also help in improving your general problem solving ability. You can download the pdf form of them and practice at your own pace.

1.0Download NCERT Solutions Class 8 Maths Chapter 5 Squares and Square Root Exercise 5.1: Free PDF

The NCERT Solutions for Class 8 Maths Chapter 5 Exercise 5.1 is available for download here. The solutions provided are in a step by step manner to improve your conceptual understanding too. Download the FREE PDF from below:

2.0Key Concepts in Exercise 5.1 of Class 8 Maths Chapter 5

This exercise focuses on identifying and understanding square numbers. Below are the hep concepts covered in this exercise.

• Finding squares of natural numbers
• Properties of square numbers
• Patterns in square numbers
• Ending digits and square numbers
• Even and odd square numbers
• Number of zeros in square numbers

3.0NCERT Class 8 Maths Chapter 5: Other Exercises

4.0NCERT Class 8 Maths Chapter 5 Exercise 5.1: Detailed Solutions

• What will be the unit digit of the squares of the following numbers? (i) 81 (ii) 272 (iii) 799 (iv) 3853 (v) 1234 (vi) 26387 (vii) 52698 (viii) 99880 (ix) 12796 (x) 55555

Sol. The unit digit of the squares of the given numbers is shown against the number in the following table:

• The following numbers are not perfect squares. Give reason. (i) 1057 (ii) 23453 (iii) 7928 (iv) 222222 (v) 64000 (vi) 89722 (vii) 222000 (viii) 505050

Sol. A number that ends either with $2,3,7$ or 8 cannot be a perfect square. Also, a number that ends with odd number of zero(s) cannot be a perfect square. (i) Since the given number 1057 ends with 7, so it cannot be a perfect square. (ii) Since the given number 23453 ends with 3 , so it cannot be a perfect square. (iii) Since the given number 7928 ends with 8, so it cannot be a perfect square. (iv) Since the given number 222222 ends with 2 , so it cannot be a perfect square. (v) Since the given number 64000 ends with odd number of ' 0 ', so it cannot be a perfect square. (vi) Since the given number 89722 ends with 2, so it cannot be a perfect square. (vii) Since the given number 222000 ends with odd number of ' 0 ', so it cannot be a perfect square. (viii) Since the given number 505050 ends with odd number of ' 0 ', so it cannot be a perfect square. 3. The squares of which of the following would be odd numbers? (i) 431 (ii) 2826 (iii) 7779 (iv) 82004

Sol. (i) The given number 431 is odd, so its square must be odd. (ii) The given number 2826 is even, so its square must be even. (iii) The given number 7779 is odd, so its square must be odd. (iv) The given number 82004 is even, so its square must be even. 4. Observe the following pattern and find the missing digits:

$\begin{array}{rl}& 11^2=121\\ & 101^2=10201\\ & 1001^2=1002001\\ & 100001^2=1\dots \dots ..................\end{array}.$

Sol. The missing digits are as under: $100001^2=10000200001$ $10000001^2=100000020000001$ 5. Observe the following pattern and find the missing numbers:

$\begin{array}{rl}& 11^2=121\\ & 101^2=10201\\ & 10101^2=102030201\\ & 1010101^2=\\ & \dots ...........{}^2=10203040504030201\end{array}$

Sol. $1010101^2=1020304030201$ $101010101^2=10203040504030201$ 6. Using the given pattern, find the missing numbers: $1^2+2^2+2^2=3^2$ $2^2+3^2+6^2=7^2$ $3^2+4^2+12^2=13^2$ $4^2+5^2+$ _ ${}^2=21^2$ $5^2+\dots +30^2=31^2$ $6^2+7^2+{}^2={}^2$ Sol. The missing numbers are us under: $4^2+5^2+20^2=21^2$ $5^2+6^2+30^2=31^2$ $6^2+7^2+42^2=43^2$ 7. Without adding, find the sum: (i) $1+3+5+7+9$ (ii) $1+3+5+7+9+11+13+15+17+19$ (iii) $1+3+5+7+9+11+13+15+17+9+21+23$

Sol. (i) $1+3+5+7+9=$ Sum of first 5 odd numbers $=5^2=25$ (ii) $1+3+5+7+9+11+13+15+17+19$ $=$ Sum of first 10 odd numbers $=10^2=100$ (iii) $1+3+5+7+9+11+13+15+17+19+21$ $+23=$ Sum of first 12 odd numbers $=12^2=$ 144 8. (i) Express 49 as the sum of 7 odd numbers. (ii) Express 121 as the sum of 11 odd numbers.

Sol. (i) $49=7^2=1+3+5+7+9+11+13$ (ii) $121=11^2=1+3+5+7+9+11+13+15+17+19+21$ 9. How many numbers lie between squares of the following numbers? (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100

Sol. (i) Between $12^2(=144)$ and $13^2(=169)$ there are twenty four (i.e., $2\times 12$ ) numbers. (ii) Between $25^2(=625)$ and $26^2(=676)$, there are 50 (i.e. $2\times 25$ ) numbers. (iii) Between $99^2(=9801)$ and $100^2(=$ 10000), there are '198' (i.e. $2\times 99$ ) numbers.

5.0Key Features and Benefits of Class 8 Maths Chapter 5 Exercise 5.1

• The exercise 5.1 introduces square numbers with simple and clear examples.
• They strictly adhere to the current NCERT Maths syllabus for Class 8.
• The questions in the exercise are from the NCERT text books.
• Regular practice of these helps develop speed and accuracy in recognising square numbers.
• Supports preparation for Math Olympiads and competitive exams.
• Develops a strong base for higher-level study of algebra and number theory.