Algebra and number system are closely connected topics. In algebra, we deal with binomial equations having two degree, which mean highest power is two for he unknown variable. To solve this equation, we need to know how to calculate the squares and square root of the number. Likewise, square root (except from perfect squares) are part of irrational numbers, which mean number which cannot be represented like p/q format (as we saw in the rational number chapter). Study of rational numbers and irrational numbers are important, because both of them are part of real numbers, and they can be marked on number line.

Grade 8 squares and square roots chapter teaches us how to calculate square of number, and how to find square root of a number . It show different methods like factorization and long division to calculate square roots of any given number. This chapter has been best covered in Class 8 Maths NCERT book, which give detailed examples and exercises to learn to calculate square root and squares.

NCERT books are recommended course text books for students following Indian curriculum. They have been followed by CBSE and all other major school boards in India and abroad. Almost all of the public and private schools recommend this books to their students.

In this article, we have discussed about the Class 8 maths NCERT exercises for squares and square root chapter. We have provided detailed video solutions of NCERT problems for Class 8. Students can look into solved NCERT exercises for class 8 mathematics.

Though squares and square roots chapter looks easy, but many students make mistake in finding square root of a numbers, especially those which are not perfect square. These solved NCERT problems for class 8 will help in clearing the concepts of square and square root chapter, and also make student understand in how to avoid common mistakes in squares and square root chapter.

## Class 8 math ncert solution squares and square roots chapter

**Exercise 6.1 solutions**

Q1 – 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 View Answer

Q2 – The following numbers are obviously not perfect squares. Give reason.(i) 1057 (ii) 23453 (iii) 7928 (iv) 222222(v) 64000 (vi) 89722 (vii) 222000 (viii) 505050 View Answer

Q3 – The squares of which of the following would be odd numbers?(i) 431 (ii) 2826 (iii) 7779 (iv) 82004 View Answer

Q4 – Observe the following pattern and find the missing digits View Answer

Q5 – Observe the following pattern and supply the missing numbers. View Answer

Q6 – Using the given pattern, find the missing numbers View Answer

Q7 – Without adding, find the sum View Answer

Q8 – (i) Express 49 as the sum of 7 odd numbers.(ii) Express 121 as the sum of 11 odd numbers. View Answer

Q9 – How many numbers lie between squares of the following numbers? View Answer

**Exercise 6.2**

Q1 – Find the square of the following numbers. (i) 32 (ii) 35 (iii) 86 (iv) 93 (v) 71 (vi) 46 View Answer

Q2 – Write a Pythagorean triplet whose one member is. (i) 6 (ii) 14 (iii) 16 (iv) 18 View Answer

**Exercise 6.3**

Q1 – What could be the possible ‘one’s’ digits of the square root of each of the following numbers? View Answer

Q2 – Without doing any calculation, find the numbers which are surely not perfect squares View Answer

Q3 – Find the square roots of 100 and 169 by the method of repeated subtraction. View Answer

Q4 – Find the square roots of the following numbers by the Prime Factorisation Method View Answer

Q5 – For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained View Answer

Q6 – For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square. Also find the square root of the square number so obtained View Answer

Q7 – The students of Class VIII of a school donated Rs 2401 in all, for Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class. View Answer

Q8 – 2025 plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row. View Answer

Q9 – Find the smallest square number that is divisible by each of the numbers 4, 9 and 10. View Answer

Q10 – Find the smallest square number that is divisible by each of the numbers 8, 15 and 20. View Answer

**Exercise 6.4**

Q1 – Find the square root of each of the following numbers by Division method View Answer

Q2 – Find the number of digits in the square root of each of the following numbers (without any calculation). View Answer

Q3 – Find the square root of the following decimal numbers. View Answer

Q4 – Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained. View Answer

Q5 – Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained View Answer

Q6 – Find the length of the side of a square whose area is 441 m2 View Answer

Q7 – In a right triangle ABC, ∠B = 90°. (a) If AB = 6 cm, BC = 8 cm, find AC (b) If AC = 13 cm, BC = 5 cm, find AB View Answer

Q8 – A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this. View Answer

Q9 – There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement. View Answer

## End Note

In the article, we have shared solutions for ncert exercises for class 8 maths for squares and square roots chapter. Students can click to respective chapters and refer to the right solution. We advise students to refer to them as clearing their concepts, and matching their solutions. Student should not use them to copy solutions for their homework and instead should try to solve homework on own, as it will impact their learning process.

In case you have any doubts regarding solution, or need further clarification, you can write to us. You can also reach out to us, in case you have doubt in other text books’ problems or school exam papers. We will be glad to assist you in helping with your doubt.

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