EXTRA QUESTIONS FOR CLASS 9 MATHS CHAPTER -1 NUMBER SYSTEM WITH ANSWERS

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 $1.3\overline{2}+\text{}0.\overline{35}$ 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 $0.6+0.\overline{7}+0.4\overline{7}$ 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 : $\frac{30}{5\sqrt{3}-3\sqrt{5 }}$

14. Simplify : $\frac{2\sqrt{3}}{\sqrt{3}-\sqrt{2}}+\frac{3\sqrt{2}}{\sqrt{3}+\sqrt{2 }}$

15. Find the value of ‘a’ and ‘b’ if,$\frac{7+3\sqrt{5}}{3+\sqrt{5}}+\frac{7-3\sqrt{5}}{3-\sqrt{5}}=a+\sqrt{5}b$

16. Simplify : (i) ${\left(\sqrt{5}+\sqrt{2}\right)}^2$ (ii) ${\left(81\right)}^{\frac{1}{4}}-8{\left(216\right)}^{\frac{1}{3}}+15{\left(32\right)}^{\frac{1}{5}}+\sqrt{225 }$

17. Simplify :
$\begin{array}{l}\end{array}$i) 6−4 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 $aandb.$

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