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 1√11.

2. Rationalize 1√37.

3. Rationalize 1√17.

4. Rationalize 1√23.



5. Rationalize 1√46.

6. Rationalize 1√37.

7. Rationalize 11+√3.

8. Rationalize 11+√7.

9. Rationalize 14+√13.

10. Rationalize 17+√29.

11. Rationalize 111βˆ’βˆš13.

12. Rationalize 19βˆ’βˆš57.

13. Rationalize 113βˆ’βˆš15.

14. Rationalize 1√13βˆ’βˆš11.

15. Rationalize 1√21βˆ’βˆš29

16. Rationalize 1√31+√41.

17. Rationalize 1√21+√37.

18. Rationalize 2√5+√7.

19. Rationalize 5√28+√37.

20. Rationalize 6√53βˆ’βˆš49.

21. Rationalize 17√53βˆ’βˆš49.

22. Rationalize the denominator and find the conjugate of the fraction so formed- 1√5βˆ’βˆš4.

23. Rationalize the denominator and find the conjugate of the resulting fraction- 2√11βˆ’βˆš9.

24. Rationalize the fraction and find the conjugate of the resulting fraction- 6√21βˆ’βˆš19.

25. Rationalize the given fraction and find the conjugate of the resulting fraction- 10√59βˆ’βˆš41.

26. Rationalize the fraction and find the conjugate of the resulting fraction- 1921βˆ’βˆš41.

27. Find the value of β€˜a’ in the given equation:

      1√17βˆ’βˆš15 = √a+√152


28. Find the value of β€˜a’ in the given equation:

      1√19βˆ’βˆš12 = √19+√a7


29. Find the value of β€˜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:

      11√8+15√21.



Solutions:


1. √1111

2. √3737

3. √1717

4. √2323

5. √4646

6. √7171

7. √3βˆ’12

8. √7βˆ’16

9. 4βˆ’βˆš133

10. 7βˆ’βˆš2920

11. 11+√13108

12. 9+√5724

13. βˆ’13βˆ’βˆš152

14. √13+√112

15. √29βˆ’βˆš218

16. √41βˆ’βˆš3110

17. √37βˆ’βˆš2116

18. √37βˆ’βˆš2116

19. 5(√37βˆ’βˆš28)9

20. 3(√53+7)2

21. 17(√53+7)4

22. √5βˆ’βˆš41

23. √11+√91

24. 3(√19βˆ’βˆš21)1

25. 5(√41βˆ’βˆš59)9

26. 19(√41βˆ’21)400

27. a = √17

28. a = √12

29. a = 107

30. βˆ’171βˆ’7√3βˆ’78√2546

31. 477√2βˆ’2√15βˆ’455106

32. 231+120√21168


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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