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.**

**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

● **Square**

**Perfect Square or Square Number**

● **Square - Worksheets**

**8th Grade Math Practice** **Math Homework Sheets** **From Worksheet on Squares to HOME PAGE**

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