rationalisation basic sums for practice number systems 9th cbse work sheets

1. Rationalize 111√$\frac{1}{\sqrt{11}}$.

2. Rationalize 137√$\frac{1}{\sqrt{37}}$.

3. Rationalize 117√$\frac{1}{\sqrt{17}}$.

4. Rationalize 123√$\frac{1}{\sqrt{23}}$.

. Rationalize 146√$\frac{1}{\sqrt{46}}$.

6. Rationalize 137√$\frac{1}{\sqrt{37}}$.

7. Rationalize 11+3√$\frac{1}{1+\sqrt{3}}$.

8. Rationalize 11+7√$\frac{1}{1+\sqrt{7}}$.

9. Rationalize 14+13√$\frac{1}{4+\sqrt{13}}$.

10. Rationalize 17+29√$\frac{1}{7+\sqrt{29}}$.

11. Rationalize 111−13√$\frac{1}{11-\sqrt{13}}$.

12. Rationalize 19−57√$\frac{1}{9-\sqrt{57}}$.

13. Rationalize 113−15√$\frac{1}{13-\sqrt{15}}$.

14. Rationalize 113√−11√$\frac{1}{\sqrt{13}-\sqrt{11}}$.

15. Rationalize 121√−29√$\frac{1}{\sqrt{21}-\sqrt{29}}$. 

16. Rationalize 131√+41√$\frac{1}{\sqrt{31}+\sqrt{41}}$.

17. Rationalize 121√+37√$\frac{1}{\sqrt{21}+\sqrt{37}}$.

18. Rationalize 25√+7√$\frac{2}{\sqrt{5}+\sqrt{7}}$.

19. Rationalize 528√+37√$\frac{5}{\sqrt{28}+\sqrt{37}}$.

20. Rationalize 653√−49√$\frac{6}{\sqrt{53}-\sqrt{49}}$.

21. Rationalize 1753√−49√$\frac{17}{\sqrt{53}-\sqrt{49}}$.

22. Rationalize the denominator and find the conjugate of the fraction so formed- 15√−4√$\frac{1}{\sqrt{5}-\sqrt{4}}$.

23. Rationalize the denominator and find the conjugate of the resulting fraction- 211√−9√$\frac{2}{\sqrt{11}-\sqrt{9}}$.

. Rationalize 146√$\frac{1}{\sqrt{46}}$.

6. Rationalize 137√$\frac{1}{\sqrt{37}}$.

7. Rationalize 11+3√$\frac{1}{1+\sqrt{3}}$.

8. Rationalize 11+7√$\frac{1}{1+\sqrt{7}}$.

9. Rationalize 14+13√$\frac{1}{4+\sqrt{13}}$.

10. Rationalize 17+29√$\frac{1}{7+\sqrt{29}}$.

11. Rationalize 111−13√$\frac{1}{11-\sqrt{13}}$.

12. Rationalize 19−57√$\frac{1}{9-\sqrt{57}}$.

13. Rationalize 113−15√$\frac{1}{13-\sqrt{15}}$.

14. Rationalize 113√−11√$\frac{1}{\sqrt{13}-\sqrt{11}}$.

15. Rationalize 121√−29√$\frac{1}{\sqrt{21}-\sqrt{29}}$. 

16. Rationalize 131√+41√$\frac{1}{\sqrt{31}+\sqrt{41}}$.

17. Rationalize 121√+37√$\frac{1}{\sqrt{21}+\sqrt{37}}$.

18. Rationalize 25√+7√$\frac{2}{\sqrt{5}+\sqrt{7}}$.

19. Rationalize 528√+37√$\frac{5}{\sqrt{28}+\sqrt{37}}$.

20. Rationalize 653√−49√$\frac{6}{\sqrt{53}-\sqrt{49}}$.

21. Rationalize 1753√−49√$\frac{17}{\sqrt{53}-\sqrt{49}}$.

22. Rationalize the denominator and find the conjugate of the fraction so formed- 15√−4√$\frac{1}{\sqrt{5}-\sqrt{4}}$.

23. Rationalize the denominator and find the conjugate of the resulting fraction- 211√−9√$\frac{2}{\sqrt{11}-\sqrt{9}}$.

. 11√+9√1$\frac{\sqrt{11}+\sqrt{9}}{1}$

24. 3(19√−21√)1$\frac{3(\sqrt{19}-\sqrt{21})}{1}$

25. 5(41√−59√)9$\frac{5(\sqrt{41}-\sqrt{59})}{9}$

26. 19(41√−21)400$\frac{19(\sqrt{41}-21)}{400}$

27. a = √17

28. a = √12

29. a = 107

30. −171−73√−782√546$\frac{-171-7\sqrt{3}-78\sqrt{2}}{546}$

31. 4772√−215√−455106$\frac{477\sqrt{2}-2\sqrt{15}-455}{106}$

32. 231+12021√168$\frac{231+120\sqrt{21}}{168}$