Math, asked by durgesh4992, 11 months ago

rationalise the denominator 4√3+5√2/ √48+√18

Answers

Answered by Mihir1001

$\huge{\underline{\mathfrak{\textcolor{blue}{Answer :}}}}$

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

$\LARGE{\underline{\mathrm{\textcolor{red}{Step-by-step \: \: explanation :}}}}$

We have,

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

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

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

$\Large{ = \frac{48 - 12 \sqrt{6} + 20 \sqrt{6} - 30}{48 - 18} }$

$\Large{ = \frac{(48 - 30) + (20 - 12) \sqrt{6} }{30} }$

$\Large{ = \frac{18 + 8 \sqrt{6} }{30} }$

$\Large{ = \frac{2(9 + 4 \sqrt{6} )}{2(15)} }$

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

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