NCERT Solutions Class 9 Maths Chapter 1 Number System Exercise 1.5

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.

1.0Download NCERT Solutions of Class 9 Maths Chapter 1 Number System Exercise 1.5: Free PDF

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:

2.0NCERT Exercise Solutions Class 9 Chapter 1- Number Systems: All Exercises 

3.0NCERT Class 9 Maths Chapter 1 Exercise 1.5 : Detailed Solutions

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

4.0Key Features and Benefits Class 9 Maths Chapter 1 Number System: Exercise 1.5

1. Solving these NCERT Solutions will help you to learn how to rationalise denominators.
2. Solutions provided here are following the latest NCERT syllabus and are useful for CBSE exams.
3. They provide simple to follow explanations to make the concept simple and clear to understand.
4. Continuous practice of NCERT Solutions will make these types of questions easy to solve.
5. It assists with sharpening your maths for Olympiad and other competitive exams.