Question

9)
Rationalise the denominator of
​

Answer 1

Step-by-step explanation:

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

On rationalizing the denominator,

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

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

$\frac{16 \times 3 - 20 \sqrt{6} + 12 \sqrt{6} - 15 \times 2 }{16 \times 3 - 9 \times 2}$

$\frac{48 - 8 \sqrt{6} - 30}{48 - 18}$

$\frac{ 12 - 8 \sqrt{6} }{30}$

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

$\frac{ 6 - 4 \sqrt{6} }{15}$

I hope it is helpful