Dynamic Classes
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Worksheet Name: Rationalisation Standard: 9th Subject: Mathematics
Q1. If x = 2 + √3, find the value of x + . 1
Q2. If x = , find the value of 4x + 2x
√3+1
3 2
− 8x + 7.
2
Q3. If x = 3 + √8, find the value of x 2
+
1
2
.
x
Q4. If x = 2 + √3, find the value of x 3
+
1
3
.
x
Q5. Simplify:
7+3√5 7−3√5
−
3+√5 3−√5
Q6. Find the value of 6
, it being given that √3 = 1.732 and √5 = 2.236.
√5−√3
Q7. If a = √2 + 1, then write the value of a − 1
a
.
Q8. Simplify:
3√2−2√3 √12
+
3√2+2√3 √3−√2
Q9. In each of the following determine rational numbers a and b:
4+3√5
= a + b√5
4−3√5
Q10. Rationales the denominator and simplify:
1+√2
3−2√2
Q11. Simplify:
√5+√3 √5−√3
+
√5−√3 √5+√3
Q12. Rationales the denominator and simplify:
4√3+5√2
√48+√18
Q13. Express each one of the following with rational denominator:
Dynamic Classes
16
√41−5
Q14. In the following determine rational numbers a and b:
3+√2
= a + b√2
3−√2
Q15. Rationales the denominator and simplify:
2√3−√5
2√2+3√3
Q16. In each of the following determine rational numbers a and b:
5+3√3
= a + b√3
7+4√3
Q17. Rationales the denominator and simplify:
5+2√3
7+4√3
Q18. In each of the following determine rational numbers a and b:
√11−√7
= a − b√77
√11+√7
Q19. In the following determine rational numbers a and b:
4+√2
= a − √b
2+√2
Q20. If x = √2 − 1, then write the value of . 1
Q21. In each of the following determine rational numbers a and b:
√3−1
= a − b√3
√3+1
Q22. Rationales the denominator and simplify:
√3−√2
√3+√2
Q23. If √3−1
= x + y√3, find the value of x and y.
√3+1
Q24. Retionalise the denominator of each of the following:
1
√12
Q25. Simplify the following expression:
2
(√3 + √7)
Q26. Simplify the following expression:
2
(√5 − √3)
Q27. Express each one of the following with rational denominator:
1
√6−√5
Q28. Retionalise the denominator of each of the following:
3√2
√5
Q29. Simplify the following expression:
(√5 − 2)(√3 − √5)
Q30. Simplify the following expression:
2
(2√5 + 3√2)
Q31. Simplify the following expression:
(√5 − √2)(√5 + √2)
Q32. Simplify the following expression:
(11 + √11)(11 − √11)
Q33. Retionalise the denominator of each of the following:
3
2√5
Q34. Simplify the following expression:
(3 + √3)(5 − √2)
Q35. Simplify the following expression:
(5 + √7)(5 − √7)
Q36. Simplify the following expression:
(3 + √3)(3 − √3)
Q37. Simplify the following:
3 3
√4 × √16
Q38. Express each one of the following with rational denominator:
1
3+√2
Dynamic Classes
Q39. Write the rationalisation factor of √5 − 2.
Q40. Simplify the following expression:
(√8 − √2)(√8 + √2)
Q41. Simplify the following expression:
(4 + √7)(3 + √2)
Q42. Simplify: √3 − 2√2.
Q43. Retionalise the denominator of each of the following:
√2+√5
√3
Q44. Write the rationalisation factor of 7 − 3√5.
Q45. Simplify: √3 + 2√2.
Q46. Write the reciprocal 5 + √2.
Q47. Write the value of (2 + √3)(2 − √3).
Q48. Retionalise the denominator of each of the following:
√3+1
Q49. Retionalise the denominator of each of the following:
√2
√5
Q50. Express each one of the following with rational denominator:
1
2√5−√3
