Question

plzzz do this..........​

Answer 1

We have

$\implies \bf \dfrac{7 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{48} + \sqrt{18} }$

$\implies \bf \dfrac{7 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{2 \times 2 \times 2 \times 2 \times3} + \sqrt{2 \times 3 \times 3} }$

$\implies \bf \dfrac{7 \sqrt{3} - 5 \sqrt{2} }{ \sqrt{2 ^{2} \times 2^{2} \times3} + \sqrt{2 \times 3^{2} } }$

$\implies \bf \dfrac{7 \sqrt{3} - 5 \sqrt{2} }{ 2 \times 2\sqrt{ 3} +3 \sqrt{2 } }$

$\implies \bf \dfrac{7 \sqrt{3} - 5 \sqrt{2} }{ 4\sqrt{ 3} +3 \sqrt{2 } }$

Multiplying by 4√3-3√2 on both numerator and denominator, we get

$\implies \bf \dfrac{7 \sqrt{3} - 5 \sqrt{2} }{ 4\sqrt{ 3} +3 \sqrt{2 } } \times \dfrac{4 \sqrt{3} - 3 \sqrt{2} }{ 4\sqrt{ 3} - 3 \sqrt{2 } }$

$\implies \bf \dfrac{(7 \sqrt{3} - 5 \sqrt{2} ) \times( 4 \sqrt{3} - 3 \sqrt{2})}{ (4\sqrt{ 3} )^{2} - (3 \sqrt{2 }) ^{2} }$

$\implies \bf \dfrac{(7 \sqrt{3} - 5 \sqrt{2} ) \times( 4 \sqrt{3} - 3 \sqrt{2})}{ (48 - 18) }$

$\implies \bf \dfrac{(7 \sqrt{3} - 5 \sqrt{2} ) \times( 4 \sqrt{3} - 3 \sqrt{2})}{ 30 }$

$\implies \bf \dfrac{(7 \sqrt{3} \times 4 \sqrt{3} - 7 \sqrt{3} \: \times 3 \sqrt{2} - 5 \sqrt{2} \times 4 \sqrt{3} + 5 \sqrt{2} \times 3 \sqrt{2})}{ 30 }$

$\implies \bf \dfrac{(84-21 \sqrt{6} - 20 \sqrt{6} + 30 )}{ 30 }$

$\red{\implies \bf \dfrac{114-41 \sqrt{6} }{ 30 } }$