RD Sharma Solutions Class 10 Real Numbers Exercise 1.5

RD Sharma Class 10 Solutions Chapter 1 Ex 1.5 PDF Free Download

Exercise 1.5

1. Show that the following numbers are irrational.

(i) \(\frac{1}{\sqrt{2}}\)

(ii) \(7\sqrt{5}\)

(iii) \(6+\sqrt{2}\)

(iv) \(3-\sqrt{5}\)

Solution:

(i) \(\frac{1}{\sqrt{2}}\)

class 10 maths chapter 1 real numbers exercise 1.5-1

(ii) \(7\sqrt{5}\)

class 10 maths chapter 1 real numbers exercise 1.5-2

(iii) \(6+\sqrt{2}\)

class 10 maths chapter 1 real numbers exercise 1.5-3

(iv) \(3-\sqrt{5}\)

class 10 maths chapter 1 real numbers exercise 1.5-4

2. Prove that the following numbers are irrationals.

(i) \(\frac{2}{\sqrt{7}}\)

(ii) \(\frac{3}{2\sqrt{5}}\)

(iii) \(4+\sqrt{2}\)

(iv) \(5\sqrt{2}\)

Solution:

(i) \(\frac{2}{\sqrt{7}}\)

class 10 maths chapter 1 real numbers exercise 1.5-5

(ii) \(\frac{3}{2\sqrt{5}}\)

class 10 maths chapter 1 real numbers exercise 1.5-6

(iii) \(4+\sqrt{2}\)

class 10 maths chapter 1 real numbers exercise 1.5-7

(iv) \(5\sqrt{2}\)

class 10 maths chapter 1 real numbers exercise 1.5-8

3. Show that \(2-\sqrt{3}\) is an irrational number.

Solution:

class 10 maths chapter 1 real numbers exercise 1.5-9

4. Show that \(3+\sqrt{2}\) is an irrational number.

Solution:

class 10 maths chapter 1 real numbers exercise 1.5-10

5. Prove that \(4-5\sqrt{2}\) is an irrational number.

Solution:

class 10 maths chapter 1 real numbers exercise 1.5-11

6. Show that \(5-2\sqrt{3}\) is an irrational number.

Solution:

class 10 maths chapter 1 real numbers exercise 1.5-12

7. Prove that \(2\sqrt{3}-1\) is an irrational number.

Solution:

class 10 maths chapter 1 real numbers exercise 1.5-13

8. Prove that \(2-3\sqrt{5}\) is an irrational number.

Solution:

class 10 maths chapter 1 real numbers exercise 1.5-14

9. Prove that \(\sqrt{5}+\sqrt{3}\) is irrational.

Solution:

class 10 maths chapter 1 real numbers exercise 1.5-15

10. Prove that \(\sqrt{3}+\sqrt{4}\) is irrational.

Solution:

class 10 maths chapter 1 real numbers exercise 1.5-16

11. Prove that for any prime positive integer p, \(\sqrt{p}\) is an irrational number.

Solution:

class 10 maths chapter 1 real numbers exercise 1.5-17

12. If p, q are prime positive integers, prove that \(\sqrt{p}+\sqrt{q}\) is an irrational number.

Solution:

class 10 maths chapter 1 real numbers exercise 1.5-18

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