Worksheet on Number System for Class 9

Numbers are everywhere around us, students discover the amazing world of grade 9 printable number system practice questions that explore rational numbers, irrational numbers, and real numbers. These worksheets help learners understand number operations, properties, and relationships through clear examples. Every problem builds confidence in mathematical thinking and problem-solving skills. Students can download a free Class 9 number system worksheet PDF for extra practice.

Solved Questions on Number System

1. Which of the following compares of the surds A = √7 + √6 and B = √5 + √8?

a) A < B                          
b) A > B
c) A = B                          
d) A² = B² + 2

Answer: b) A > B

Explanation: By squaring both the surds we get,

A² = (√7 + √6)² = 7 +  6 +  2√42   =  13 + 2√42 ………….(1)
B² = (√5 + √8)² = 5 +  8 +  2√40   = 13 + 2√40  ………….(2)
Also, √42 > √40

Comparing equation (1) and (2),                        
⇒ 13 + 2√42 > 13 + 2√40       
⇒ A² > B²

∴ A > B

2. Simplify: (4 + √7) (7 + √10)

a) 28 + 4√10 + 6√7 + 2√70
b) 28 + 4√10 + 7√7 + 2√70
c) 28 + 4√10 + 6√7 + √70
d) 28 + 4√10 + 7√7 + √70

Answer: d) 28 + 4√10 + 7√7 + √70

Explanation: Using the identity,

(√p + √q) (√r + √s) = √pr + √ps + √qr + √qs

(4 + √7) (7 + √10) = 28 + 4√10 + 7√7 + √70

3. Rationalise the numerator of the following expression:

a) 
b) 
c) 
d) 

Answer: c) 

Explanation:

4. Simplify the following by the method of rationalising:

a) 2 + 3√2 + 2√6 + √12
b)2 −3√2 + 2√6 + √12
c)2 + 3√2−2√6 + √12
d) 2 + 3√2 + 2√6 −√12

Answer:  a) 2 + 3√2 + 2√6 + √12

Explanation:

5. What is the value of x in the following equation?

a) 2/k
b) 3/k
c) 4/k
d) 5/k

Answer: a) 2/k

Explanation: By cross-multiplying both sides, we get:

xk = [√3 +√ 12 + √ 4+√ 9] × [√ 3+√ 12 − √ 4−√ 9]

xk = [(√3 +√ 12) + (√ 4+√ 9)] × [(√ 3+√ 12) − (√ 4 +√ 9)]

Using the formula, (a + b) × (a − b) = a² − b², we get:

xk = [(√ 3+√ 12)² − (√ 4 + √ 9)²]

xk = (3 + 12 + 2√36) − (4 + 9 +  2√ 36)

xk = 15 + 2√ 36 − 13 − 2√ 36

xk = 2

∴ x = 2/k