Question

rationalise the denominator of 4√3+5√2/4√3+3√2 ​

Answer 1

$\large\bf\underline\red{Question \: :- }$

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

$\large\bf\underline\red{Answer \: :- }</h3><h3>$

How to rationalize

Let assume

$\small\sf{ \frac{a + b}{c +d } \longmapsto \frac{a + b}{c + d} \times \frac{a - b}{a - b} }$

Substitute value

$\longmapsto\sf{ \frac{4 \sqrt{3} + 5 \sqrt{2} }{ \sqrt{3} + 3 \sqrt{2} } } \\ \\ \longmapsto\sf{\frac{4 \sqrt{3} + 5 \sqrt{2} }{ \sqrt{3} + 3 \sqrt{2} } \times \frac{ \sqrt{3} - 3 \sqrt{2} }{ \sqrt{3} - 3 \sqrt{2} } } \\ \\ \longmapsto\sf{ \frac{(4 \sqrt{3} + 5 \sqrt{2} )( \sqrt{3} - 3 \sqrt{2}) }{( \sqrt{3} + 3 \sqrt{2} )(</strong><strong>3 - 3\sqrt{2} )} }$

In denominator we use formula :

(a+b) (a-b) = a²-b²

$\longmapsto\sf{ \frac{4 \sqrt{3}( \sqrt{3} - 3 \sqrt{2} ) + 5 \sqrt{2} ( \sqrt{3} - 3 \sqrt{2} )}{( \sqrt{3} ) {}^{2} - (3 \sqrt{2}) {}^{2} } } \\ \\ \longmapsto\sf{ \frac{4 \sqrt{9} - 12 \sqrt{6} + 5 \sqrt{6} - 15 \sqrt{4} }{3 - 9 \sqrt{4} } } \\ \\ \longmapsto\sf{ \frac{4(3) + 7 \sqrt{6} - 15(2) }{3 - 9(2)} } \\ \\\longmapsto\sf{ \frac{12 + 7 \sqrt{6} - 30}{3 - 18} }$

${\large{\underline{\boxed{\bf{\leadsto{\red{ \: \frac{7 \sqrt{6} - 18 }{ - 15} }}}}}}}$

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Answer 2

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

Step-by-step explanation:

Please check image attached below.