Question

if 1.732 find value root 2= 1.414 and root 3 = 1.732 find value of 4/3 root 3+2 root2 + 3/3 root 3-2 root 2

Answer 1

$$\begin{gathered} Given\sqrt{2}=4.414and\sqrt{3}=1.732 \\ \frac{4}{3\sqrt{3}+2\sqrt{2}}+\frac{3}{3\sqrt{3}-2\sqrt{2}} \\ =\frac{4(3\sqrt{3}-2\sqrt{2})+3(3\sqrt{3}+2\sqrt{2})}{(3\sqrt{3}+2\sqrt{2})(3\sqrt{3}-2\sqrt{2})} \\ =\frac{12\sqrt{3}-8\sqrt{2}+9\sqrt{3}+6\sqrt{2}}{(3\sqrt{3}{)}^2-(2\sqrt{2}{)}^2} \\ =\frac{21\sqrt{3}-2\sqrt{2}}{27-8} \\ =\frac{21\sqrt{3}-2\sqrt{2}}{19} \\ =\frac{21\times 1.732-2\times 1.414}{19} \\ =\frac{36.372-2.828}{19} \\ =\frac{33.544}{19} \\ =1.765 \end{gathered}$$