K C Sisodia Solutions for Chapter: Pure Arithmetic, Exercise 1: TEST YOUR SKILLS

Without actual division, find the following fraction is terminating decimal or not.

$\frac{44}{63}$

If $x=\frac{3+\sqrt{7}}{2}$, find the value of $4x^2+\frac{1}{x^2}$.

If $x=\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$and  $y=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}$, find the value of $x^2+y^2$. 

Simplify:$\left\{\frac{3\sqrt{2}}{\sqrt{6}+\sqrt{3}}+\frac{\sqrt{6}}{\sqrt{3}+\sqrt{2}}-\frac{4\sqrt{3}}{\sqrt{6}+\sqrt{2}}\right\}$

If $x=\frac{\sqrt{5}-2}{\sqrt{5}+2}$, then find the value of $x+\frac{1}{x}$?

If$x=\frac{\sqrt{5}-2}{\sqrt{5}+2}$  then find the value of  $x^2+\frac{1}{x^2}.$  

Simplify: $\frac{3\sqrt{7}}{\sqrt{5}+\sqrt{2}}-\frac{5\sqrt{5}}{\sqrt{2}+\sqrt{7}}+\frac{2\sqrt{2}}{\sqrt{7}+\sqrt{5}}$

If $x=1-\sqrt{2}$, find the value of ${\left(x-\frac{1}{x}\right)}^4$