#### Chapter 1 Real Numbers R.D. Sharma Solutions for Class 10th Math Exercise 1.5

**Exercise 1.5**

**Level 1**

1. Show that the following numbers are irrational.

(i) 1/√2

(ii) 7√5

(iii) 6+√2

(iv) 3-√5

2. Prove that following numbers are irrationals.

(i) 2/√7

(ii) 3/2√5

(iii) 4+√2

(iv) 5√2

3. Show that 2-√3 is an irrational number.

4. Show that 3+√2 is an irrational number.

5. Prove that 4-√5 is an irrational number.

6. Show that 5-2√3 is an irrational number.

7. Prove that 2√3-1 is an irrational number.

8. Prove that 2-3√5 is an irrational number.

9. Prove that √5+√3 is irrational.

10. Prove that √2+√3 is an irrational number.

11. Prove that for any prime positive integer p, √p is an irrational number.

12. If p, q are prime positive integers, prove that √p + √q is a irrational number.

(i) 1/√2

(ii) 7√5

(iii) 6+√2

(iv) 3-√5

**Answer**(i) 2/√7

(ii) 3/2√5

(iii) 4+√2

(iv) 5√2

**Answer**3. Show that 2-√3 is an irrational number.

**Answer**4. Show that 3+√2 is an irrational number.

**Answer**5. Prove that 4-√5 is an irrational number.

**Answer**6. Show that 5-2√3 is an irrational number.

**Answer**7. Prove that 2√3-1 is an irrational number.

**Answer**8. Prove that 2-3√5 is an irrational number.

**Answer**9. Prove that √5+√3 is irrational.

**Answer**10. Prove that √2+√3 is an irrational number.

**Answer****Level 2**11. Prove that for any prime positive integer p, √p is an irrational number.

**Answer**12. If p, q are prime positive integers, prove that √p + √q is a irrational number.

**Answer**