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From previous topics of irrational numbers it has become clear that rationalization of denominator is one of the most important steps done while doing calculations which involve irrational denominators. In the previous topic of rationalization we have learnt how to rationalize the denominator. In this topic, we will get to solve some problems regarding rationalization of denominators. Below are given some problems involving calculation of rationalization of denominator:
1. Rationalize 1β11.
2. Rationalize 1β37.
3. Rationalize 1β17.
4. Rationalize 1β23.
5. Rationalize 1β46.
6. Rationalize 1β37.
7. Rationalize 11+β3.
8. Rationalize 11+β7.
9. Rationalize 14+β13.
10. Rationalize 17+β29.
11. Rationalize 111ββ13.
12. Rationalize 19ββ57.
13. Rationalize 113ββ15.
14. Rationalize 1β13ββ11.
15. Rationalize 1β21ββ29.
16. Rationalize 1β31+β41.
17. Rationalize 1β21+β37.
18. Rationalize 2β5+β7.
19. Rationalize 5β28+β37.
20. Rationalize 6β53ββ49.
21. Rationalize 17β53ββ49.
22. Rationalize the denominator and find the conjugate of the fraction so formed- 1β5ββ4.
23. Rationalize the denominator and find the conjugate of the resulting fraction- 2β11ββ9.
24. Rationalize the fraction and find the conjugate of the resulting fraction- 6β21ββ19.
25. Rationalize the given fraction and find the conjugate of the resulting fraction- 10β59ββ41.
26. Rationalize the fraction and find the conjugate of the resulting fraction- 1921ββ41.
27. Find the value of βaβ in the given equation:
1β17ββ15 = βa+β152
28. Find the value of βaβ in the given equation:
1β19ββ12 = β19+βa7
29. Find the value of βaβ in the given equation:
211+β14 = \frac{2(11-\sqrt{14})}{a}\)
30. Solve the following problem:
19+β3+13+β2.
31. Solve the following arithematic:
211+β15+92+β8.
32. Solve the following:
11β8+15β21.
Solutions:
1. β1111
2. β3737
3. β1717
4. β2323
5. β4646
6. β7171
7. β3β12
8. β7β16
9. 4ββ133
10. 7ββ2920
11. 11+β13108
12. 9+β5724
13. β13ββ152
14. β13+β112
15. β29ββ218
16. β41ββ3110
17. β37ββ2116
18. β37ββ2116
19. 5(β37ββ28)9
20. 3(β53+7)2
21. 17(β53+7)4
22. β5ββ41
23. β11+β91
24. 3(β19ββ21)1
25. 5(β41ββ59)9
26. 19(β41β21)400
27. a = β17
28. a = β12
29. a = 107
30. β171β7β3β78β2546
31. 477β2β2β15β455106
32. 231+120β21168
Irrational Numbers
Definition of Irrational Numbers
Representation of Irrational Numbers on The Number Line
Comparison between Two Irrational Numbers
Comparison between Rational and Irrational Numbers
Problems on Irrational Numbers
Problems on Rationalizing the Denominator
Worksheet on Irrational Numbers
From Worksheet on Irrational Numbers to HOME PAGE
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