Question

Rationalize the denominator
$\frac{3}{2 \sqrt{5} - 3 \sqrt{2} }$
Please answer step by step​

Answer 1

Step-by-step explanation:

We have,

$\tt{ \dfrac{3}{2 \sqrt{5} - 3 \sqrt{2} } }$

$\tt{ = \dfrac{3( 2 \sqrt{5} + 3 \sqrt{2} )}{(2 \sqrt{5} - 3 \sqrt{2} )( 2 \sqrt{5} + 3 \sqrt{2} )} }$

$\tt{ = \dfrac{3( 2 \sqrt{5} + 3 \sqrt{2} )}{(2 \sqrt{5} )^{2} -( 3 \sqrt{2} )^{2} } }$

$\tt{ = \dfrac{3( 2 \sqrt{5} + 3 \sqrt{2} )}{20 -18 } }$

$\tt{ = \dfrac{3( 2 \sqrt{5} + 3 \sqrt{2} )}{2} }$

Answer 2

Answer:

Step-by-step explanation:

$\Large{\mathsf{\frac{3}{2 \sqrt{5} - 3 \sqrt{2}}}}$

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

$\Large{\mathsf{ \frac{6 \sqrt{5} + 9 \sqrt{2} }{ {(2 \sqrt{5}) }^{2} - {( 3 \sqrt{2} )}^{2} } }}$

$\Large{\mathsf{ \frac{6 \sqrt{5} + 9 \sqrt{2} }{20 - 18} }}$

$\Large{\mathsf{ \frac{6 \sqrt{5} + 9 \sqrt{2} }{2} }}$