Math, asked by ayushiM06, 7 months ago

How to rationalise this part

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Answered by kuldeep20941

Step-by-step explanation:

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See The Attachment My Friend....

×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=×=

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Answered by Mihir1001

$\bold{Answer:}$

$\huge\boxed{ \frac{8 \sqrt{6} + 4 \sqrt{15} + 3 \sqrt{10} + 12}{9} }$

$\bold{Step-by-step-explaination:}$

we have,

$\frac{4 \sqrt{3} + 3 \sqrt{2} }{6 \sqrt{2} - 3 \sqrt{5} }$

$= \frac{(4 \sqrt{3} + 3 \sqrt{2} ) \times (6 \sqrt{2} + 3 \sqrt{5} )}{(6 \sqrt{2} - 3 \sqrt{5} ) \times (6 \sqrt{2} + 3 \sqrt{5} )}$

$= \frac{(4 \sqrt{3} )(6 \sqrt{2} ) + (4 \sqrt{3} )(3 \sqrt{5} ) + (3 \sqrt{2} )(6 \sqrt{2} ) + (3 \sqrt{2} )(3 \sqrt{5} )}{ {(6 \sqrt{2} )}^{2} - {(3 \sqrt{5} )}^{2} }$

$= \frac{24 \sqrt{6} + 12 \sqrt{15} + 36 + 9 \sqrt{10} }{72 - 45}$

$= \frac{(3)(8 \sqrt{6} + 4 \sqrt{15} + 3 \sqrt{10} + 12)}{27}$

$= \frac{(3)(8 \sqrt{6} + 4 \sqrt{15} + 3 \sqrt{10} + 12)}{(3)(9)}$

$= \frac{8 \sqrt{6} + 4 \sqrt{15} + 3 \sqrt{10} + 12}{9}$

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