R.D. Sharma Solutions Class 10th: Ch 1 Real Numbers Exercise 1.5

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

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


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