Solutions of chapter 3. Squares and Square Roots | RS Aggarwal - Mathematics

1

Using the prime factorization method, find which of the following numbers perfect squares are:

(i) 441 (ii) 576

(iii) 11025 (iv) 1176

(v) 5625 (vi) 9075

(vii) 4225 (viii) 1089

2

Show that each of the following numbers is a perfect square. In each case, find the number whose square is the given number:

(i) 1225

(ii) 2601

(iii) 5929

(iv) 7056

(v) 8281

3

By what least number should the given number be multiplied to get a perfect square number? In each case, find the number whose square is the new number.

(i) 3675 (ii) 2156

(iii) 3332 (iv) 2925

(v) 9075 (vi) 7623

(vii) 3380 (viii) 2475

4

By what least number should the given number be divided to get a perfect square number? In each case, find the number whose square is the new number.

(i) 1575 (ii) 9075

(iii) 4851 (iv) 3380

(v) 4500 (vi) 7776

(vii) 8820 (viii) 4056

5

Find the largest number of 2 digits which is a perfect square.

6

Find the largest number of 3 digits which is a perfect square.

1

Give reason to show that none of the numbers given below is a perfect square:

(i) 5372 (v) 360

(ii) 5963 (vi) 64000

(iii) 8457 (vii) 2500000

(iv) 9468

2

Which of the following are squares of even numbers?

(i) 196 (ii) 441 (iii) 900 (v) 324

(iv) 625

3

Which of the following are squares of odd numbers?

(i) 484 (ii) 961 (iii) 7396 (iv) 8649 (v) 4225

4

Without adding, find the sum:

(i) (1 + 3 + 5 + 7 + 9 + 11 + 13)

(ii) (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19)

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

5

Express 81 as the sum of 9 odd numbers

5

Express 100 as the sum of 10 odd numbers

6

Write a Pythagorean triplet whose smallest member is:

(i) 6 (ii) 14 (iii) 16 (iv) 20

7

Evaluate:

(i) (38)² - (37)² (ii) (75)² - (74)²

(iii) (92)² - (91)² (iv) (105)² - (104)²

(v) (141)² -(140)² (vi) (218)² - (217)²

8

Using the formula (a + b)² = (a² + 2ab + b²), evaluate:

(i) (310)² (ii) (508)²

(iii) (630)²

9

Using the formula (a - b)² = (a² - 2ab + b²), evaluate:

(i) (196)² (ii) (689)² (iii) (891)²

10

Evaluate:

(i) 69 × 71 (ii) 94 × 106.

11

Evaluate:

(i) 88 × 92 (ii) 78 × 82.

12

Fill in the blanks:

(i) The square of an even number is….

(ii) The square of an odd number is…….

(iii) The square of a proper fraction is ………..than the given fraction.

(iv) n² = the sum of first n ……. natural numbers.

13

Write (T) for true and (F) for false for each of the statements given below:

(i) The number of digits in a perfect square is even.

(ii) The square of a prime number is prime.

(iii) The sum of two perfect squares is a perfect square.

(iv) The difference of two perfect squares is a perfect square.

(v) The product of two perfect squares is a perfect square.

1

Find the value of each of the following, using the column method:

(23)²

2

Find the value of each of the following, using the column method:

(35)²

3

Find the value of each of the following, using the column method:

(52)²

4

Find the value of each of the following, using the column method:

(96)²

5

Find the value of each of the following, using the diagonal method:

(67)²

6

Find the value of each of the following, using the diagonal method:

(86)²

7

Find the value of each of the following, using the diagonal method:

(137)²

8

Find the value of each of the following, using the diagonal method:

(256)²

1