# Class 9 Number Systems Important Questions

Number Systems Important Questions

1. Find three rational number between $\frac{3}{4}$ and $\frac{5}{6}$ .
2. Represent √ 6.4 on the number line.
3. If x = $\frac{2&space;-&space;\sqrt{5}}{2&space;+&space;\sqrt{5}}$ and y = $\frac{2&space;+&space;\sqrt{5}}{2&space;-&space;\sqrt{5}}$ , find the value of x2 + y2 + xy.
4. Express 6.234 in the form of p/q.
5. If x = $2&space;+&space;\sqrt{3}$ , find the value of $x^{2}&space;+&space;\frac{1}{x^{2}}$ .
6. Find the smallest of the numbers $\sqrt[3]{6}$ , $\sqrt[3]{24}$ and $\sqrt[4]{8}$ .
7. Find three irrational numbers between $\frac{1}{7}$ and $\frac{2}{7}$ .
8. If x = $\frac{\sqrt{p&space;+&space;q}&space;+&space;\sqrt{p&space;-&space;q}}{\sqrt{p&space;+&space;q}&space;-&space;\sqrt{p&space;-&space;q}}$ , then find the value of qx2 -2px + q.
9. If 2a = 3b = 6c then show that c = $\frac{ab}{a + b}$ .
10. Represent $\sqrt{3}$ on the number line .