Question

If √2 = 1.414, √3 = 1.732, then find the value of 4/(3√3-2√2)+3/(3√3+2√2).

Answer 1

Rationalising

$\frac{4}{3 \sqrt{3} - 2 \sqrt{2} } \times \frac{3 \sqrt{3} + 2 \sqrt{2} }{3 \sqrt{3} + 2 \sqrt{2} } \\ \\ = > \frac{4( 3\sqrt{3} + 2 \sqrt{2} ) }{27 - 8} \\ \\ = \frac{4(3 \sqrt{3} + 2 \sqrt{2}) }{19} \\ \\ = \frac{12 \sqrt{3} + 8 \sqrt{2} }{19}$
and
$\frac{3}{3 \sqrt{3} + 2 \sqrt{2} } \\ \\ = \frac{3(3 \sqrt{3} - 2 \sqrt{2} )}{27 - 8} \\ \\ = > \frac{3(3 \sqrt{3} - 2 \sqrt{2}) }{19} \\ = \frac{9 \sqrt{3} - 6 \sqrt{2} }{19}$
adding,

$\frac{12 \sqrt{3} + 8 \sqrt{2} }{19} + \frac{9 \sqrt{3} - 6 \sqrt{2} }{19} \\ \\ = > \frac{21 \sqrt{3} + 2 \sqrt{2} }{19}$
now putting the value we get


$\frac{21 \times 1.732 + 2 \times 1.414}{19} \\ = \frac{36.372 + 2.828}{19} \\ = \frac{39.2}{19}$
hope it helps dear friend ☺️✌️✌️