# Number Systems

Practice Questions in Irrational numbers, real numbers, exponents
1. #### Prime Factorise & Rationalise Denominator

$\frac{14}{{\sqrt {108}} - {\sqrt {96}} + {\sqrt {192}} - {\sqrt {54}}}\\$

2. #### Rational numbers - Fractions

Find 5 rational numbers between $\frac{3}{4}$ and $\frac{4}{5}$.

3. #### Operation on real numbers & Algebraic identities

If x = $\frac{3 - {\sqrt{13}}}{2}\\$, what is the value of $x^2 + \frac{1}{x^2}\\$?

4. #### Rationalise & find value of cubic expression

If x = $\frac{1}{8-\sqrt{60}}\\$, what is the value of $x^{3}-5x^{2}+8x-4?\\$

5. #### Rationalise the denominator

$\frac{1}{9 + {\sqrt{5} + \sqrt{6}}}\\$