Worksheet on Squares

In worksheet on squares we will practice many questions on perfect squares, squares of even numbers, squares of odd numbers and also on evaluating squares. 

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

(i) 225

(ii) 189

(iii) 441

(iv) 729

(v) 1575

(iv) 900

2. Show that none of the following is a perfect square: Give reason in each case.

(i) 62

(ii)143

(iii) 217

(iv) 168

(v) 90

(vi) 4000

3. Which of the following are the squares of even numbers?

(i) 196

(ii) 441

(iii) 400

(iv) 324

(v) 625

(vi) 169

4. Which of the following are the squares of odd numbers?

(i) 121

(ii) 225

(iii) 196

(iv) 484

(v) 529

5. Evaluate:

(i) (38)² - (37)²

(ii) (75)² - (74)²

(iii) (92)² - (911)²

(iv) (105)² - (194)²

(v) (141)² - (140)²

(vi) (218)² - (217)²

6. Without adding, find the sum:

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

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

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

7. (i) Express 64 as the sum of eight odd numbers.

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

8. Write a Pythagorean triplet whose smallest member is

(i) 6

(ii) 14

(iii) 16

(iv) 20

9. 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 number.

10. Show that 1450 is not a perfect square.

11. Is 15625 a perfect square?

12. 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 perfect square.

Answers of worksheet on squares are given below.

Answer:

1. (i),       (iii),       (iv),       (vi) 

3. (i),       (iii),       (iv)


4. (i),       (ii),       (v)


5. (i) 75

(ii) 149

(iii) 183

(iv) 209

(v) 281

(vi) 435


6. (i) 36

(ii) 100

(iii) 144


7. (i) 64 = 8² = (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15)

(ii) 121 = (11)² = (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21)


8. (i) (6, 8, 10)

(ii) (14, 48, 50)

(iii) (16, 63, 65)

(iv) (20, 99, 101)


9. (i) even

(ii) odd

(iii) smaller

(iv) odd


10. ending in one zero


11. Yes


12. (i) False

(ii) False

(iii) False

(iv) False

(v) Ture

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