Question

$\frac{1}{3\sqrt{5}+2\sqrt{2} =? }$

$\frac{12}{4\sqrt{3}-\sqrt{2} }$

Answer 1

#1

$\begin{gathered}\\ \sf\longmapsto \frac{1}{3 \sqrt{5} + 2 \sqrt{2} }\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto \frac{1}{3 \sqrt{5} + 2 \sqrt{2} } \times \frac{3 \sqrt{5} - 2 \sqrt{2} }{3 \sqrt{5} - 2 \sqrt{2} }\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto \frac{1(3 \sqrt{5} - 2 \sqrt{2}) }{(3 \sqrt{5} + 2 \sqrt{2}) \times (3 \sqrt{5} - 2 \sqrt{2} ) }\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto \frac{(3 \sqrt{5} - 2 \sqrt{2}) }{(3 \sqrt{5} + 2 \sqrt{2}) \times (3 \sqrt{5} - 2 \sqrt{2} ) }\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto \frac{3 \sqrt{5} - 2 \sqrt{2} }{9 \times 5 - 4 \times 2}\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto \frac{3 \sqrt{5} - 2 \sqrt{2} }{45 - 8} \end{gathered}$

$\begin{gathered}\\ \sf\longmapsto \frac{3 \sqrt{5} - 2 \sqrt{2} }{37} \end{gathered}$

______________________________

#2

$\begin{gathered}\\ \sf\longmapsto \frac{12}{4\sqrt{3}-\sqrt{2} }\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto \frac{12}{4 \sqrt{3} - \sqrt{2} } \times \frac{4 \sqrt{3} + \sqrt{2} }{4 \sqrt{3} + \sqrt{2} } \end{gathered}$

$\begin{gathered}\\ \sf\longmapsto \frac{12(4 \sqrt{3} + \sqrt{2}) }{(4 \sqrt{3} - \sqrt{2}) \times (4 \sqrt{3} + \sqrt{2} )}\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto \frac{12(4 \sqrt{3} + \sqrt{2} )}{16 \times 3 - 2}\end{gathered}$

$\begin{gathered}\\ \sf\longmapsto \frac{12(4 \sqrt{3} + \sqrt{2} )}{46}\end{gathered}$

⚜️Reduce the fraction with 2

$\begin{gathered}\\ \sf\longmapsto \frac{6(4 \sqrt{3} + \sqrt{2}) }{23}\end{gathered}$

• Multiply 6 with 4 and 1
• It is known as distributing it through parentheses
• We will multiply it with 1 because there is no number with $\sqrt{2}$

$\begin{gathered}\\ \sf\longmapsto \frac{24 \sqrt{3} + 6 \sqrt{2} }{23}\end{gathered}$

Both solved✓