WORKSHEET ON SQUARES AND SQUARE ROOTS

Find the squares of the following numbers

1)  Write the first five square numbers.  

Solution

2)  Find the square of 3/8

Solution

3)  Find the square of 5.5                       

Solution

4)  Find the square of 0.7                       

Solution

5)  196 is the square of

(A)  11     (B)  12     (C)  14     (D)  16

Solution

6)  The square of 2.8 is 78.4 ?

(A)  True     (B)  False     (C)  None of these

Solution

7)  The Square of 500 will have ----------- zeroes.

Solution

8) Write down the unit digits of the squares of the following numbers:

(i) 24              (ii) 78          (iii) 35

Solution

9)  The digit at the ones place of 572 is

Solution

10)  The units digit in the square of 1294 is  

Solution

11)  Which of the following will have 1 at its unit place ? 

(A)  192     (B)  172     (C)  182    (D)  162

Solution

12)  There are ------- perfect squares between 1 and 100.

Solution

13)  Find the perfect square numbers between

(i) 10 and 20 (ii) 50 and 60 (iii) 80 and 90.

14)  1000 is a perfect square ?

(A)  True     (B)  False     (C)  None of these

Solution

15)  Which of the following is not a perfect square ?

(A)  361     (B)  1156     (C)  1128     (D)  1681

Solution

16)  Show that 500 is not a perfect square

Solution

17)  Check whether 90 is a perfect square or not by using prime factorization.

Solution

18) Which of the following is a square of an even number ?

(A)  144     (B)  169     (C)  441     (D)  625

Solution

19)  Which of the following is a square of an odd number ?

(A)  256     (B)  361     (C)  144     (D)  400

Solution

20)  A perfect square can never have the following digit at ones place.

(A)  1     (B)  6     (C)  5     (D)  3

Solution

21)  Find the least number of four digits that is a perfect square.

Solution

22)  Find the greatest number of three digits that is a perfect square.

Solution

23)  Find the smallest perfect square divisible by 3, 4, 5 and 6.

Solution

Answers :

1)  1, 4, 9, 16, 25

2)  9/64 

3)  30.25

4)   0.49

5)  14

6)  false

7)  zeroes

8)  (i) 6  (ii) 4  (iii)  5

9)  9

10)  6

11)  192

12)  8

13)  (i) 16  (ii) no  (iii)  81

14)  false

15)  1128

16)  proved

17)  Not a perfect square

18)  144

19)  361

20)  3

21)  1024

22)  961

23)  900


Find the square root of the following numbers using prime factorization

Questions :

1)  324

2)  625

3)  400

4)  144

5)  1024 

6)  256

7)   2025

8)  36

9)   3136

10)  11025

11)  4761

Answers :

1)  18               Solution

2)  25              Solution

3)  20              Solution

4)  12               Solution

5)  32              Solution

6)  16               Solution

7)  45              Solution

8)  6                Solution

9)  56               Solution

10)  105            Solution

11)  69              Solution

Find the square root of the following numbers using long division

Questions :

1)  12321

2)  16384

3)  65536

4)  474721

5)  145161

6)  2116

7)  55225

8)  7744

9)  106276

10)  278784

Answers :

1)  111

2)  128

3)  256

4)  689

5)  381

6)  46

7)  235

8)  88

9)  326

10)  528

Solution

Simplify the following square root expressions

Questions :

1)  √64 + √196

2)  √40 + √160

3)  2√425 - 3√68

4)  √243 - 5√12 + √27 

5)  -√117 - √52 

6)  (√17)(√51)

7)  (√35)(2√15)

8)  (14√117) ÷ (7√52)

9)  (7√5)2

10)  √(176 + √2401)

Answers :

1)  22              Solution

2)  6√10          Solution

3)  4√17          Solution

4)  2√3           Solution

5)  -5√13        Solution

6)  17√3         Solution

7)  10√21       Solution

8)   3             Solution

9)  245          Solution

10)  15          Solution     

Word problems on square roots

Problem 1 :

You have a square blanket that has an area of 1600 square inches. What is the length of 1 side of the blanket ?

Problem 2 :

A square coffee table has an area of 196 square inches. What is the length of one side of the coffee table ?

Problem 3 :

You have a square flower garden that has an area of 400 square yards. What is the length of one side of the garden ?

Problem 4 :

A square desktop has an area of 324 square inches. What is the length of one side of the desktop ?

Problem 5 :

You want to carpet a square room that has an area of 144 square feet. What is the length of one side of the room ? 

Problem 6 :

You are going to decorate one wall of your bedroom  by putting border along the top. The wall is a square wall with an area of 256 square feet. What is the length of  border you need for the top of this on wall ?

Problem 7 :

To the nearest tenth, what is the square root of 33 ?

Problem 8 :

The area of a square tile is 50 square centimeters. To the nearest tenth of a centimeter, how long is one side of this tile ?

Problem 9 :

Jason's square bedroom has an area of 90 square feet. The length of one side of his room is between what two whole numbers ?

Problem 10 :

Grandma's square garden has an area of 90 square feet. The length of one side of her garden would be between what two whole numbers ? What is the length of this side to the nearest tenth of a foot ?

Solution

Answers :

1)  400 inches

2)  14 inches

3)   20 yards

4)  18 inches

5)  12 feet

6)  16 feet

7)  5.7

8)  7.1 cm

9)  9.48 feet

10)  9.5 feet

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