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Worksheet on Irrational Numbers

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 111.

2. Rationalize 137.

3. Rationalize 117.

4. Rationalize 123.



5. Rationalize 146.

6. Rationalize 137.

7. Rationalize 11+3.

8. Rationalize 11+7.

9. Rationalize 14+13.

10. Rationalize 17+29.

11. Rationalize 11113.

12. Rationalize 1957.

13. Rationalize 11315.

14. Rationalize 11311.

15. Rationalize 12129

16. Rationalize 131+41.

17. Rationalize 121+37.

18. Rationalize 25+7.

19. Rationalize 528+37.

20. Rationalize 65349.

21. Rationalize 175349.

22. Rationalize the denominator and find the conjugate of the fraction so formed- 154.

23. Rationalize the denominator and find the conjugate of the resulting fraction- 2119.

24. Rationalize the fraction and find the conjugate of the resulting fraction- 62119.

25. Rationalize the given fraction and find the conjugate of the resulting fraction- 105941.

26. Rationalize the fraction and find the conjugate of the resulting fraction- 192141.

27. Find the value of ‘a’ in the given equation:

      11715 = a+152


28. Find the value of ‘a’ in the given equation:

      11912 = 19+a7


29. Find the value of ‘a’ in the given equation:

      211+14 = \frac{2(11-\sqrt{14})}{a}\)


30. Solve the following problem:

      19+3+13+2.


31. Solve the following arithematic:

      211+15+92+8.


32. Solve the following:

      118+1521.



Solutions:


1. 1111

2. 3737

3. 1717

4. 2323

5. 4646

6. 7171

7. 312

8. 716

9. 4133

10. 72920

11. 11+13108

12. 9+5724

13. 13152

14. 13+112

15. 29218

16. 413110

17. 372116

18. 372116

19. 5(3728)9

20. 3(53+7)2

21. 17(53+7)4

22. 541

23. 11+91

24. 3(1921)1

25. 5(4159)9

26. 19(4121)400

27. a = √17

28. a = √12

29. a = 107

30. 17173782546

31. 4772215455106

32. 231+12021168


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

Rationalization

Problems on Irrational Numbers

Problems on Rationalizing the Denominator

Worksheet on Irrational Numbers





9th Grade Math

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