Question

rationalise the denominator of the following​

Answer 1

$\sf\dfrac{7 \sqrt{3} - \sqrt{2} }{ \sqrt{48} + \sqrt{18} }$

• On Rationalising the Denominator

$~~~~~:~~\implies \sf\dfrac{7 \sqrt{3} - \sqrt{2} }{ \sqrt{48} + \sqrt{18} } \times \dfrac{ \sqrt{48} - \sqrt{18} }{ \sqrt{48} - \sqrt{18} }$

${~~~~~:~~\implies \sf\dfrac{7 \sqrt{3}( \sqrt{48} - \sqrt{18})- \sqrt{2}( \sqrt{48} - \sqrt{18}) }{ { \sqrt{ {48}^{2} } } - \sqrt{ {18}^{2} } } }$

$~~~~~:~~\implies \sf\dfrac{7 \times 12 - 7\sqrt{54}- \sqrt{96} + 6 }{ 48 - 18 }$

$~~~~~:~~\implies \sf\dfrac{84 + 6 - 7\sqrt{54}- \sqrt{96} }{ 30 }$

${~~~~~:~~\implies \sf\dfrac{90 - 7\sqrt{2 \times 3 \times 3 \times 3 }- \sqrt{2 \times 2 \times 2 \times2 \times 2 \times 3 } }{ 30 }}$

$~~~~~:~~\implies \sf\dfrac{90 - 21\sqrt{6 }- 4\sqrt{ 6 } }{ 30 }$

$~~~~~:~~\implies \sf\dfrac{90 - 25\sqrt{6 } }{ 30 }$

$~~~~~:~~\implies \sf\dfrac{5(18 - 5\sqrt{6 }) }{ 5(6) }$

$~~~~~:~~\implies \sf\dfrac{18 - 5\sqrt{6 } }{ 6 }$

$\boxed{ \sf\dfrac{7 \sqrt{3} - \sqrt{2} }{ \sqrt{48} + \sqrt{18} } = \bf\dfrac{18 - 5\sqrt{6 } }{ 6 } }$