Question

Rationalize the denominator of 4root3+5root2/root48+root18​

Answer 1

Answer:

$\frac{9 + 4 \sqrt{6} }{15}$

Step-by-step explanation:

$\frac{4 \sqrt{3} + 5 \sqrt{2} }{4 \sqrt{3} + 3 \sqrt{2} }$

Rationalising the Denominator.

$\frac{(4 \sqrt{3} + 5 \sqrt{2})(4 \sqrt{3} - 3 \sqrt{2}) }{(4 \sqrt{3} + 3 \sqrt{2})( 4 \sqrt{3} - 3 \sqrt{2}) }$

$\frac{48 - 12 \sqrt{6} + 20 \sqrt{6} - 30}{(4 \sqrt{3})^2 - (3 \sqrt{2} )^2}$

$\frac{18 + 8 \sqrt{6} }{48 - 18}$

$\frac{2(9 + 4 \sqrt{6} )}{30}$

$\frac{9 + 4 \sqrt{6} }{15}$