CBSE Class 9 Mathematics Number System Worksheet Set 04

CBSE Class 9 Mathematics Worksheet - Number System (3)

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1. Visualize 3.756 on the number line, using successive magnification

2. Represent √3.5 on the number line

3. If x = 3+2√2, find the value of x2 + 1/x2 (34)

4. If x = 2 + √5, Prove that x2 + 1 = 18

X2

5. Express 1. 3 2 + 0.35 as a fraction in simplest form. (166/99)

6. Rationalise the denominator 1

√6 + √5 - √11

7. If a and b are rational numbers, find a and b

a) √2 + √3 = a + b √6 (a=2, b=5/6)

3 √2 - 2√3

b) √5 – 2 - √5 + 2 = a + b √5 (a = 0, b = - 8)

√5 + 2 √5 – 2

8. Simplify: a) 1 + 1 + 1

1 + √2 √2 + √3 √3 + √4 (1)

9. If a = √3+√2 and b = √3 – √2, find the value of a2 + b2 (98)

√3 – √2 √3 + √2

2

10. If a = 9 - 4√5, find the value of a – 1/a (320)

3

11. If x = 1 - √2, find the value of x – 1/x (8)

12. If x = 3 + 2 √2, find the value of √x - 1 (8)

√x

13. If x = 0.125, find the value of (1/x) 1/3

14. If x = √3 + √2 then find the value of x2 (49 + 20√6)

√3 - √2

15. If x = 1 , find the value of x3 – 2x2 – 7x + 5 (3)

2 - √3

16. Find four rational numbers between 3/5 and 4/5

17. Find two irrational numbers lying between √2 and √3

18. Find two rational and irrational numbers between 0.3101 and 0.3222

19. Simplify the following: a) 576 - 1/2 b) 343 -1/3 c) (-1/27) - 2/3 d) (0.008)4/3 e) (729)- 1/6

625 1000

20. Simplify and express the result in the simplest form: (25)3/2 x (243)2/5 (1125/512)

(16)5/4 x (8)4/3

21. Find the value x, if 5x -3 x 3 2x – 8 = 225 (x = 5)

22. Solve: a) 49 x 7x = (343)1/3 (x = -1)

b) 2x = (128)1/7 x (√2)4 (3)

c) If 3x = 9 , find x (1/2)

27x

d) (1/7)4 – 2x = √7 (9/4)

23. Evaluate: a) 125 -1/3 x 271/3 (62 +82 )1/2 (6)

b) (172 – 82)1/2 (15)

c) 641/3 (641/3 – 642/3)

24. Simplify: a) √45 + √80 - 3√20 (√5)

b) 7√6 - √252 - √294 + 6√7 ( 0 )

c) 4√28 + 3√7

25. Give an example of two irrational numbers whose: (A) Sum is rational (B) product is rational (C) quotient is rational

PREPARED BY: MAHABOOB PASHA IX –XBOYS

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