Number System Grade IX - 3

Self Assessment Test 3

Based on Chapter 1

Time: 1 hour

M.M. 25

Note: Q. 1 - 2 carry 1 mark each, Q. 3 - 5 carry 2 marks each, Q. 6-8 carry 3 marks each and Q.9 - 10 carry 4 marks each.

1. Find the product: $(3-\sqrt{5})(3+\sqrt{5})$.

2. Express $0.3\overline{47}$ (recurring decimal) in the form $\frac{p}{q}$, where p and q are integers and $q \neq 0$.

3. Find a point corresponding to $\frac{5}{2} + \sqrt{3}$ on the number line.

4. Rationalise the denominator of $\frac{1}{\sqrt{5}+\sqrt{2}}$ and subtract it from $\sqrt{5}-\sqrt{2}$.

5. Evaluate:

   (i) $(32768)^{\frac{1}{5}}$

   (ii) $\left(\frac{-1}{27}\right)^{-\frac{1}{3}}$

6. Simplify: $8\sqrt{18} + 4\sqrt{72} - 5\sqrt{32} + 3\sqrt{98} + 2\sqrt{50}$.

7. Find two irrational numbers in decimal form between $\sqrt{2}$ and $2$.

8. If $\sqrt{5}=2.236$ and $\sqrt{20}=4.472$, find the value of $\frac{49}{\sqrt{125}-\sqrt{45}}$.

9. If $\frac{(\sqrt{2}-3)}{(\sqrt{2}+3)} - \frac{(\sqrt{2}+3)}{(\sqrt{2}-3)} = e + f\sqrt{2}$, find e and f where e and f are rational numbers.

10. If $z = 5 + 2\sqrt{6}$, find:

    (i) $\sqrt{z} + \frac{1}{\sqrt{z}}$

    (ii) $\sqrt{z} - \frac{1}{\sqrt{z}}$