ICSE Class 9 Maths Selina Solutions Chapter 1 Rational And Irrational Numbers

ICSE Class 9 Maths Selina Solutions Chapter 1: ICSE Class 9 Maths Selina Solutions Chapter 1 focuses on rational and irrational numbers. It helps students understand the differences between these types of numbers and their unique properties.

ICSE Class 9 Maths Selina Solutions Chapter 1 Rational And Irrational Numbers Overview

ICSE Class 9 Maths Selina Solutions Chapter 1 PDF

ICSE Class 9 Maths Selina Solutions Chapter 1 PDF

ICSE Class 9 Maths Selina Solutions Chapter 1 Rational And Irrational Numbers

ICSE Class 9 Maths Selina Solutions Chapter 1 Exercise 1(A) PAGE: 4

1. Is zero a rational number? Can it be written in the form p/q, where p and q are integers and q ≠ 0?

Solution:

2. Are the following statements true or false? Give reasons for your answers.

(i) Every whole number is a natural number.

(ii) Every whole number is a rational number.

(iii) Every integer is a rational number.

(iv) Every rational number is a whole number.

Solution:

3. Arrange -5/9, 7/12, -2/3 and 11/18 in the ascending order of their magnitudes. Also, find the difference between the largest and the smallest of these rational numbers. Express this difference as a decimal fraction correct to one decimal place.

Solution:

4. Arrange 5/8, -3/16, -1/4 and 17/32 in the descending order of their magnitudes. Also, find the sum of the lowest and the largest of these rational numbers. Express the result obtained as a decimal fraction correct to two decimal places.

Solution:

5. Without doing any actual division, find which of the following rational numbers have terminating decimal representation:

(i) 7/16

(ii) 23/125

(iii) 9/14

(iv) 32/45

(v) 43/50

(vi) 17/40

(vii) 61/75

(viii) 123/250

Solution:

1. State whether the following numbers are rational or not:

(i) (𝟐 + √𝟐) ^𝟐

(ii) (𝟑 − √𝟑) ^𝟐

(iii) (𝟓 + √𝟓)(𝟓 − √𝟓)

(iv) (√𝟑 − √𝟐) ^𝟐

(v) (3/2√𝟐) ²

(vi) (√7/6√𝟐) ²

Solution:

2. Find the square of:

(i) 3√2/5

(ii) √3 + √2

(iii) √5 – 2

(iv) 3 + 2√5

Solution:

3. State, in each case, whether true or false:

(i) √𝟐 + √𝟑 = √𝟓

(ii) 2√4 + 2 = 6

(iii) 𝟑√𝟕 − 𝟐√𝟕 = √𝟕

(iv) 𝟐/7 is an irrational number.

(v) 𝟓/11 is a rational number.

(vi) All rational numbers are real numbers.

(vii) All real numbers are rational numbers.

(viii) Some real numbers are rational numbers.

Solution:

4. Given universal set is {-6, -5¾, -√4, -3/5, -3/8, 0, 4/5, 1, 1⅔, √8, 3.01, π, 8.47}

From the given set, find:

(i) Set of Rational numbers

(ii) Set of irrational numbers

(iii) Set of integers

(iv) Set of non-negative integers

Solution:

5. Use method of contradiction to show that √𝟑 and √𝟓 are irrational.

Solution:

6. Prove that each of the following numbers is irrational:

(i) √3 + √2

(ii) 3 − √2

(iii) √5 – 2

Solution:

7. Write a pair of irrational numbers whose sum is irrational.

Solution:

8. Write a pair of irrational numbers whose sum is rational.

Solution:

9. Write a pair of irrational numbers whose difference is irrational.

Solution:

10. Write a pair of irrational numbers whose difference is rational.

Solution:

11. Write a pair of irrational numbers whose product is irrational.

Solution:

12. Write a pair of irrational numbers whose product is rational.

Solution:

13. Write in ascending order:

Solution:

14. Write in descending order:

(i) 2∜6 and 3∜2

(ii) 7√3 and 3√7

Solution:

15. Compare:

Solution:

16. Insert two irrational numbers between 5 and 6.

Solution:

17. Insert five irrational numbers between 2√5 and 3√3.

Solution:

18. Write two rational numbers between √2 and√3.

Solution:

19. Write three rational numbers between √3 and √5.

Solution:

20. Simplify each of the following:

Solution:

1. State, with reason, which of the following are surds and which are not:

Solution:

2. Write the lowest rationalizing factor of:

(i) 5√2

(ii) √24

(iii) √5 – 3

(iv) 7 – √7

(v) √18 – √50

(vi) √5 – √2

(vii) √13 + 3

(viii) 15 – 3√2

(ix) 3√2 + 2√3

Solution:

3. Rationalize the denominators of:

Solution:

4. Find the values of ‘a’ and ‘b’ in each of the following:

Solution:

5. Simplify:

Solution:

6. If x = and y = ; Find:

(i) x ²

(ii) y ²

(iii) xy

(iv) x ² + y ² = xy

Solution:

7. If m = 1/(3 – 2√2) and n = 1/(3 + 2√2), find:

(i) m ²

(ii) n ²

(iii) mn

Solution:

8. If x = 2√3 + 2√2, find:

(i) 1/x

(ii) x + 1/x

(iii) (x + 1/x) ²

Solution:

9. If x = 1 − √2, find the value of (x + 1/x) ³ .

Solution:

10. If x = 5 − 2√6, find: x ² + 1/x ²

Solution:

11. Show that:

Solution:

12. Rationalize the denominator of:

Solution:

13. If √2 = 1.4 and √3 = 1.7, find the value of each of the following, correct to

one decimal place:

(i) 1/(√3 – √2)

(ii) 1/(3 + 2√2)

(iii) (2 – √3)/√3

Solution:

14. Evaluate:

(4 – √5)/(4 + √5) + (4 + √5)/(4 – √5)

Solution:

15. If (2 + √5)/(2 – √5) = x and (2 – √5)/(2 + √5) = y; find the value of x ² – y ² .

Solution:

1. Simplify:

Solution:

2. Simplify:

Solution:

3. Evaluate, correct to one place of decimal. The expression 5/(√20 – √10), if √5 = 2.2 and √10 = 3.2.

Solution:

4. If x = √3 − √2. Find the value of:

(i) x + 1/x

(ii) x ² + 1/x ²

(iii) x ³ + 1/x ³

(iv) x ³ + 1/x ³ – 3(x ² + 1/x ² ) + x + 1/x

Solution:

( iv) x ³ + 1/x ³ – 3(x ² + 1/x ² ) + x + 1/x

5. Show that:

(i) Negative of an irrational number is irrational.

Solution:

(ii) The product of a non-zero rational number and an irrational number is an irrational number.

Solution:

6. Draw a line segment of length √5 cm.

Solution:

7. Draw a line segment of length √𝟑 cm.

Solution:

8. Draw a line segment of length √8 cm.

Solution:

9. Show that:

Solution:

10. Show that:

(i) x ³ + 1/x ³ = 52, if x = 2 + √3

(ii) x ² + 1/x ² = 34, if x = 3 + 2√2

Solution:

11. Show that x is rational if:

(i) x ² = 6

(ii) x ² = 0.009

(iii) x ² = 27

Solution:

12. Show that x is rational if:

(i) x ² = 16

(ii) x ² = 0.0004

Solution:

13. Using the following figure, show that BD = √x.

Solution:

Benefits of ICSE Class 9 Maths Selina Solutions Chapter 1

• Clear Understanding: Provides clear explanations and examples to understand the concepts of rational and irrational numbers.
• Comprehensive Coverage: Covers all important topics related to rational and irrational numbers, ensuring thorough preparation.
• Enhanced Problem-Solving Skills: Improves students ability to solve mathematical problems involving rational and irrational numbers confidently.
• Exam Preparation: Prepares students effectively for exams by providing practice questions and solutions.
• Accessible Learning: Provides a structured approach to learning, making complex concepts easier to understand.