Chapter 1 Real Numbers R.D. Sharma Solutions for Class 10th Math Exercise 1.5
Exercise 1.5
Level 1
Level 1
1. Show that the following numbers are irrational.
(i) 1/√2
(ii) 7√5
(iii) 6+√2
(iv) 3-√5
Answer
2. Prove that following numbers are irrationals.
(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
(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