# BHARDWAJ CLASSES

## CBSE CLASS 9 MATHS NUMBER SYSTEM EXTRA QUESTIONS

### Number System - Work Sheet

1. Find three rational numbers between 3/5 and 7/8 .

2. Find five rational numbers between √5/7 and 4/5 .

3. Find two irrational numbers whose –
(i) Sum is a rational number.
(ii) Sum ia an irrational number.
(iii) Difference is a rational number.
(iv) Difference is an irrational number.
(v) Product is a rational number.
(vi) Product is an irrational number.
(vii) Quotient is a rational number.
(viii) Quotient is an irrational number.

4. Let x be rational and y be irrational. Is xy necessarily an irrational? Justify your answer by an example.

5. Construct √10 on number line.

6. Insert a rational and an irrational number between 2.357 and 3.121.

7. Express $1.3\overline{2}+\text{\hspace{0.17em}}\text{​}0.\overline{35}$ as a fraction in the simplest form.

8. If x = 3 +2√2, find out whether x – 1/x is rational or irrational.

9. Show that$2.1\overline{13}$ can be expressed in the form p/q .

10. Express $18.\overline{48}$ in the form p/q .

11. Express $0.6\text{\hspace{0.17em}}+\text{\hspace{0.17em}}0.\overline{7}\text{\hspace{0.17em}}+0.4\overline{7}$ in the form p/q .

12. Visualise $1.\overline{33}$ on number line upto 3 digits after decimal.

13. Rationalise the denominator of the following :

14. Simplify :

15. Find the value of ‘a’ and ‘b’ if,

16. Simplify : (i) ${\left(\sqrt{5}+\sqrt{2}\right)}^{2}$ (ii)

17. Simplify :
$\begin{array}{l}\end{array}$i) 64 3 6+4 3 ii) 4+ 5 4 5 + 4 5 4+ 5 iii) 3 + 2 3 2 +) 3 2 3 + 2 iv) 3 4 5 3 + 2 4 5 + 3

18. If $a=\frac{4}{3-\sqrt{5}}$ , find the value of $a+\frac{1}{a}$ .

19. If $\frac{3}{4\sqrt{5}-\sqrt{3}}+\frac{2}{4\sqrt{5}+\sqrt{3}}=a\sqrt{5}+b\sqrt{3}$ , find the value of

20. Simplify  1 3 8 1 8 7 + 1 7 6 1 6 5 + 1 5 2