Question

rationalise the denominator 3√2/√15+3√2​

Answer 1

Solution:-

$\rm \: : \implies \dfrac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} }$

For rationalize multiply and divide by :- √15 - 3√2

$\rm \: : \implies \dfrac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} } \times \dfrac{ \sqrt{15} - 3 \sqrt{2} }{ \sqrt{15} - 3 \sqrt{2} }$

$\rm : \implies \dfrac{3 \sqrt{2}( \sqrt{15} - 3 \sqrt{2} )}{ (\sqrt{15}{} - 3 \sqrt{2} )( \sqrt{15} + 3 \sqrt{2}) }$

$\rm : \implies \: \dfrac{3 \sqrt{30} - (3 \sqrt{2} ) {}^{2} }{( \sqrt{15} )^{2} - (3 \sqrt{2} ) {}^{2} }$

$\rm : \implies \: \dfrac{3 \sqrt{30} - 9 \times 2 }{15 - 9 \times 2}$

$\rm : \implies \dfrac{3 \sqrt{30} - 18}{15 - 18}$

$: \implies \dfrac{3 \sqrt{30} - 18 }{ - 3}$

$\rm : \implies \dfrac{ - 3( \sqrt{30} - 6)}{3}$

$\rm \rm : \implies \dfrac{ - \not3( \sqrt{30} - 6)}{ \not3}$

Answer is

$\rm \: \to \: - (\sqrt{30} - 6)$