NCERT Solutions for Class 9 Maths Chapter 1 Number System: Exercise 1.5, teaches about rationalising the denominator, which is an important part of the chapter. This exercise will explain how to simplify expressions and remove the irrational number in the denominator.
The NCERT Solutions follow the CBSE exam pattern and are aligned with the latest NCERT Syllabus. The step by step solutions provided helps the students understand the concept clearly.
Practicing this exercise will help in getting better marks in your school exams and also prepare for competitive exams. Download the FREE PDF for a quick revision.
Get the free PDF of NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.5 here. This exercise solves questions on how to simplify expressions by rationalising the denominator. Download the free PDF from below:
1. Find:
(i) (64)¹ᐟ²
(ii) 32¹ᐟ⁵
(iii) 125¹ᐟ³
Sol. (i) (64)¹ᐟ² = (8²)¹ᐟ² = 8^(2 × 1/2) = 8¹ = 8
(ii) 32¹ᐟ⁵ = (2⁵)¹ᐟ⁵ = 2^(5 × 1/5) = 2¹ = 2
(iii) (125)¹ᐟ³ = (5³)¹ᐟ³ = 5^(3 × 1/3) = 5¹ = 5
2. Find:
(i) 9³ᐟ²
(ii) 32²ᐟ⁵
(iii) 16³ᐟ⁴
(iv) 125⁻¹ᐟ³
Sol. (i) 9³ᐟ² = (9¹ᐟ²)³ = (3)³ = 27
(ii) 32²ᐟ⁵ = (2⁵)²ᐟ⁵ = 2^(5 × 2/5) = 2² = 4
(iii) 16³ᐟ⁴ = (2⁴)³ᐟ⁴ = 2^(4 × 3/4) = 2³ = 8
(iv) 125⁻¹ᐟ³ = (5³)⁻¹ᐟ³ = 5^(3 × -1/3) = 5⁻¹ = 1/5
3. Simplify :
(i) 2²ᐟ³ ⋅ 2¹ᐟ⁵
(ii) (1/3³)⁷
(iii) 11¹ᐟ⁴ / 11¹ᐟ²
(iv) 7¹ᐟ² ⋅ 8¹ᐟ²
Sol. (i) 2²ᐟ³ ⋅ 2¹ᐟ⁵ = 2^(2/3 + 1/5) = 2^((10+3)/15) = 2¹³ᐟ¹⁵
(ii) (1/3³)⁷ = (3⁻³)⁷ = 3^(-3 × 7) = 3⁻²¹
(iii) 11¹ᐟ⁴ / 11¹ᐟ² = 11^(1/4 − 1/2) = 11^(1/4 − 2/4) = 11⁻¹ᐟ⁴
(iv) 7¹ᐟ² ⋅ 8¹ᐟ² = (7×8)¹ᐟ² = (56)¹ᐟ²
(Session 2025 - 26)