Square Root Questions And Answers

Square Root Questions is a useful topic for students who want to learn maths in a simple way. Square Root Questions help us find the number that gives a square when multiplied by itself. This topic is important because it builds a strong base in maths and improves problem solving skills. Students can practise different questions to understand how square roots work in real sums.

Square Root Formula and Rules

If x² = y, then √y = x

√y means "what number multiplied by itself gives y?"

Example:

√25 = 5 because 5 × 5 = 25

√81 = 9 because 9 × 9 = 81

Important Square Root Rules

• Rule 1: √(a × b) = √a × √b
• Rule 2: √(a/b) = √a / √b
• Rule 3: √(a²) = a (for positive a)
• Rule 4: (√a)² = a
• Rule 5: √0 = 0
• Rule 6: √1 = 1
• Rule 7: Square root of negative numbers is NOT real.

Square Root  Chart 1 to 20

Basic Square Root Questions

Question 1: Find the value of each:

a) √36    b) √144    c) √225    d) √400    e) √169

Solutions:

a) √36  = 6    (6 × 6 = 36)

b) √144 = 12   (12 × 12 = 144)

c) √225 = 15   (15 × 15 = 225)

d) √400 = 20   (20 × 20 = 400)

e) √169 = 13   (13 × 13 = 169)

Question 2: Evaluate:

a) √(64 × 9)         b) √(25 × 16)

a) √(64 × 9) = √64 × √9 = 8 × 3 = 24

b) √(25 × 16) = √25 × √16 = 5 × 4 = 20

Fill in the Missing Number

Question 3:

a) √___ = 7   

7 × 7 = 49  

Answer: 49

b) √___ = 11  

11 × 11 = 121

Answer: 121

c) √___ = 16 

16 × 16 = 256

Answer: 256

d) √___ = 25 

25 × 25 = 625

Answer: 625

e) ___² = 196 

√196 = 14

Answer: 14

True or False Questions

Question 4:

a) √49 = 7  

b) √100 = 50      

c) √(4×9) = √4+√9

d) (√15)² = 15  

e) √0 = 0       

f) √(-16) is real 

g) √81 × √4 = 18  

Answer: 

a) TRUE (7 × 7 = 49)

b) FALSE (√100 = 10, not 50)

c) FALSE (√36 = 6, not 2 + 3 = 5)

d) TRUE

e) TRUE

f) FALSE (negative number)

g) TRUE (9×2=18)

Simplifying Square Root Questions

Question 5: Simplify each expression:

a) √72

√72 = √(36 × 2)

= √36 × √2

= 6√2

b) √200

√200 = √(100 × 2)

= √100 × √2

= 10√2

c) √48

√48 = √(16 × 3)

= √16 × √3

= 4√3

d) √180

√180 = √(36 × 5)

= √36 × √5

= 6√5

Question 6: Simplify:

a) √(75/3)

= √25 = 5

b) √(98/2)

= √49 = 7

c) 3√12 + 2√27

3√12 = 3 × √(4×3)

= 3 × 2√3

= 6√3

2√27 = 2 × √(9×3)

= 2 × 3√3

= 6√3

Total = 6√3 + 6√3 = 12√3

Square Root Factorization Questions

Question 7: Find square root using prime factorisation:

a) √324

Step 1: Prime factorisation of 324

324 = 2 × 162

    = 2 × 2 × 81

    = 2 × 2 × 9 × 9

    = 2² × 3² × 3²

    = 2² × 3⁴

Step 2: Pair the factors

324 = (2 × 3²)²

    = (2 × 9)²

    = 18²

Step 3: √324 = 18

Verify: 18 × 18 = 324

b) √1764

1764 = 2 × 882

     = 2 × 2 × 441

     = 4 × 441

     = 4 × 21 × 21

     = 2² × 21²

     = (2 × 21)²

     = 42²

√1764 = 42

Verify: 42 × 42 = 1764

Estimate Square Roots

Question 8: Estimate the value of √50.

We know:

√49 = 7 (just below 50)

√64 = 8 (just above 50)

So √50 is between 7 and 8.

Since 50 is very close to 49:

√50 ≈ 7.07 (more precisely)

Method:

7² = 49

8² = 64

50 − 49 = 1

64 − 49 = 15

Estimate = 7 + (1/15) ≈ 7.07

Square Root Word Problems

Question 9: A square garden has area 256 m². Find the length of each side.

Area = side²

256 = side²

side = √256

side = 16 m

Answer: Each side = 16 m

Question 10: A square floor tile has area 196 cm². How long is each side of the tile?

side = √196

side = 14 cm

Answer: Each side = 14 cm

Question 11: 729 students are arranged in a square formation. How many students are in each row?

Students per row = √729

√729 = √(9 × 81) = 3 × 9 = 27

Answer: 27 students in each row

Verify: 27 × 27 = 729

Question 12: The area of a square is 1225 cm². Find its perimeter.

Step 1: Find side

side = √1225

√1225 = √(25 × 49) = 5 × 7 = 35 cm

Step 2: Find perimeter

Perimeter = 4 × side = 4 × 35 = 140 cm

Answer: Perimeter = 140 cm

Question 13: A right triangle has legs of 9 cm and 12 cm. Find the hypotenuse.

By Pythagoras theorem:

h² = 9² + 12²

h² = 81 + 144

h² = 225

h = √225

h = 15 cm

Answer: Hypotenuse = 15 cm

Question 14: The area of a square room is 441 m². Find the cost of laying carpet at ₹80 per m².

Step 1: Find side

side = √441 = 21 m

Step 2: Area = 441 m² (already given)

Step 3: Cost = 441 × 80 = ₹35,280

Answer: Cost = ₹35,280

Square Root MCQs

Q1: √169 = ?

a) 11    b) 12    c) 13    d) 14

Answer: c) 13 

Q2: Which of the following is a perfect square?

a) 50    b) 72    c) 144    d) 200

Answer: c) 144 (12² = 144) 

Q3: √(0.25) = ?

a) 0.5    b) 0.05    c) 5    d) 50

Answer: a) 0.5

(0.5 × 0.5 = 0.25)

Q4: If √x = 15, then x = ?

a) 225    b) 125    c) 30    d) 150

Answer: a) 225 (15² = 225) 

Q5: √72 simplified is:

a) 6√2    b) 8√2    c) 4√3    d) 6√3

Answer: a) 6√2

(√72 = √36×2 = 6√2)

Q6: A square has perimeter 60 cm. Its area is:

a) 225 cm²    b) 200 cm²    c) 144 cm²    d) 100 cm²

Solution: Side = 60/4 = 15 cm; Area = 15² = 225 cm²

Answer: a) 225 cm²

Q7: Between which two integers does √55 lie?

a) 6 and 7    b) 7 and 8    c) 8 and 9    d) 5 and 6

Solution: 7² = 49, 8² = 64; 49 < 55 < 64

Answer: b) 7 and 8

Q8: √(x²) = ?

a) x²    b) x/2    c) 2x    d) x (for positive x)

Answer: d) x 

Q9: If √(x+5) = 4, find x.

Square both sides:

x + 5 = 16

x = 11

a) 9    b) 11    c) 13    d) 15

Answer: b) 11

Q10: √(1 + √(1 + √(1))) simplified:

Step 1: Innermost = √1 = 1

Step 2: 1 + 1 = 2 → √2

Step 3: 1 + √2 ≈ 1 + 1.414 = 2.414 → √2.414 ≈ 1.554

Approximate answer ≈ 1.55

This is an approximation question.

Q11: √5625 = ?

5625 = 25 × 225 = 5² × 15² = 75²

√5625 = 75

a) 65    b) 70    c) 75    d) 80

Answer: c) 75

Square Root Worksheet Questions

Fill in the Blanks

1. √___ = 19       

2. √484 = ___      

3. √(4 × 25) = ___   

4. (√13)² = ___     

5. √___ = 25       

6. √1 = ___         

7. √0.49 = ___      

8. √(100/4) = ___   

Answer:

1. Answer: 361

2.  Answer: 22

3. Answer: 10

4. Answer: 13

5. Answer: 625

6. Answer: 1

7. Answer: 0.7

8. Answer: 5

Match the Following

Column A          Column B

√196         →        14

√289         →        17

√441         →        21

√625         →        25

√961         →        31

Answers:

√196 = 14

√289 = 17

√441 = 21

√625 = 25

√961 = 31

Short Answer Questions

Q12: Is 500 a perfect square? Show working.

√500 = √(100 × 5) = 10√5

Since 10√5 is not a whole number,

500 is NOT a perfect square.

Q13: Find √0.0016.

√0.0016 = √(16/10000)

= √16/√10000

= 4/100

= 0.04

Answer: 0.04

Download PDF - Square Root Questions

Related Topics:

• Square Root
• Square And Square Root
• NCERT Solutions Class 8 Chapter 6 Squares and Square Roots
• Important Questions Class 8 Maths Squares and Square Roots