# 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.

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

Square

Perfect Square or Square Number

Properties of Perfect Squares

Square - Worksheets

Worksheet on Squares

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

## Recent Articles

1. ### Shifting of Digits in a Number |Exchanging the Digits to Another Place

May 19, 24 06:35 PM

What is the Effect of shifting of digits in a number? Let us observe two numbers 1528 and 5182. We see that the digits are the same, but places are different in these two numbers. Thus, if the digits…

2. ### Formation of Greatest and Smallest Numbers | Arranging the Numbers

May 19, 24 03:36 PM

the greatest number is formed by arranging the given digits in descending order and the smallest number by arranging them in ascending order. The position of the digit at the extreme left of a number…

3. ### Formation of Numbers with the Given Digits |Making Numbers with Digits

May 19, 24 03:19 PM

In formation of numbers with the given digits we may say that a number is an arranged group of digits. Numbers may be formed with or without the repetition of digits.

4. ### Arranging Numbers | Ascending Order | Descending Order |Compare Digits

May 19, 24 02:23 PM

We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the sma…