Question

ratinalise the denominator ( 4√3+5√2)/(4√3+3√2)​

Answer 1

Answer:

$\frac{54+4\sqrt{6}}{15}$

Step-by-step explanation:

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

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

$\implies \frac{48+20\sqrt{6}-12\sqrt{6}+60}{(48-18)}\\\\\implies \frac{108+8\sqrt{6}}{30}\\\\\implies \frac{54+4\sqrt{6}}{15}$

DETAILS :

The question involved rationalisation .

Here we have to rationalise the denominator .

This is done so that the answer has a rational denominator.

The rational denominator can be obtained by multiplying with conjugate denominator.

Answer 2

$\huge \bf \red{ \mid{ \overline{ \underline{ANSWER}}} \mid}$

$\bf{QUESTION}$

ratinalise the denominator ( 4√3+5√2)/(4√3+3√2)​

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

$\bf {\frac{{(4 \sqrt{3})^{2} + 5 \sqrt{2} \times 4 \sqrt{3} - 3 \sqrt{2} \times 4 \sqrt{3}+5\sqrt{2}\times3\sqrt{2} }}{30} }$

$\bf{ \frac{48 + 20 \sqrt{6} - 12 \sqrt{6}+60 }{30}}$

$\bf{ \frac{48 + 8 \sqrt{6}+60 }{30}}$

$\huge \bf{ \frac{108+8 \sqrt{6} }{30}}$

$\huge \bf{ \frac{54+4\sqrt{6} }{15}}$


$\huge \bf \pink{THANKS}$