Class 8 Squares and Square Root

 Chapter 6: Squares and Square Roots

Ex 6.1

1. 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 2. 

2. 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 

3. The squares of which of the following would be odd numbers? 

(i) 431 (ii) 2826 (iii) 7779 (iv) 82004 

4. Observe the following pattern and find the missing digits. 

5. Observe the following pattern and apply the missing numbers. 

11² = 121

101² = 10201

1001² = 1002001

100001² =

10000001² =

6. Using the given pattern, find the missing numbers.

11² = 121

101² = 10201

10101² = 102030201

 1010101² =

                 = 10203040504030201

7. Without adding, find the sum. 

(i) 1 + 3 + 5 + 7 + 9 

(ii) 1 + 3 + 5 + 7 + 9 + I1 + 13 + 15 + 17 +19 

(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 

8. (i) Express 49 as the sum of 7 odd numbers. (ii) Express 121 as the sum of 11 odd numbers. 

9. How many numbers lie between squares of the following numbers?

 (i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100 

Ex 6.2 

1. Find the square of the following numbers

(i) 32 (ii) 35 (iii) 86 (iv) 93 (v) 71 

(vi) 46 

2. Write a Pythagorean triplet whose one member is

 (i) 6 (ii) 14 (iii) 16 (iv) 18

                    Chapter 6: Ex 6.1 and Ex 6.2 Squares and Square Roots Free PDF

Ex 6.3

1. What could be the possible ‘one’s’ digits of the square root of each of the following numbers?

(i) 9801 (ii) 99856 (iii) 998001 (iv) 657666025 

2. Without doing any calculation, find the numbers which are indeed not perfect squares. 

(i) 153 (ii) 257 (iii) 408 (iv) 441 

3. Find the square roots of 100 

and 169 by the method of repeated subtraction. 

4. Find the square roots of the following numbers by the Prime Factorisation Method. 

(i) 729 (ii) 400 

(iii) 1764 (iv) 4096(v) 7744 

(vi) 9604 (vii) 5929 (viii) 9216 

(ix) 529 (x) 8100 

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

(i) 252 

(ii) 180 (iii) 1008 

(iv) 2028(v) 1458 

(vi) 768 

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

(i) 252 

(ii) 2925 (iii) 396 (iv) 2645 

(v) 2800 (vi) 1620 

7. The students of Class VIII of a school donated ` 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.

8. 2025 plants are to be planted in a garden so 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. 

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

10. Find the smallest square number divisible by each number 8, 15 and 20.

                                    Chapter 6 Ex 6.3 Squares and Square Roots Free PDF download

Ex 6.4 

1. Find the square root of each of the following numbers by Division method. 

(i) 2304 (ii) 4489 (iii) 3481 (iv) 529 (v) 3249 (vi) 1369 (vii) 5776 (viii) 7921 

(ix) 576 (x) 1024 (xi) 3136 (xii) 900 

2. Find the number of digits in the square root of each of the following numbers (without any calculation). (i) 64 (ii) 144 (iii) 4489 

(v) 390625

3. Find the square root of the following decimal numbers. 

(i) 2.56 (ii) 7.29 (iii) 51.84 (iv) 42.25 (v) 31.36 

4. Find the least number which must be subtracted from each of the following numbers to get a perfect square. Also, find the square root of the perfect square so obtained. 

(i) 402 (ii) 1989 (iii) 3250 

(iv) 825 (v) 4000 

5. Find the least number which must be added to each of the following numbers to get a perfect square. Also, find the square root of the perfect square so obtained. 

(i) 525 

(ii) 1750 (iii) 252 (iv) 1825(v) 6412 

6. Find the length of the side of a square whose area is 441 m2 . 

7. 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 

8. 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. 

9. 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

                           Chapter 6: Ex 6.4 Squares and Square roots free pdf

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