Question

Please answer this..

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{\dfrac{7\sqrt{3} }{\sqrt{10}+\sqrt{3} }-\dfrac{2\sqrt{5} }{\sqrt{6}+\sqrt{5} }-\dfrac{3\sqrt{2} }{\sqrt{15}+3\sqrt{2} }}$

$\sf{=\dfrac{7\sqrt{3} (\sqrt{10}-\sqrt{3} )}{(\sqrt{10}+\sqrt{3} ) (\sqrt{10}-\sqrt{3} )}-\dfrac{2\sqrt{5}(\sqrt{6}-\sqrt{5} ) }{(\sqrt{6}+\sqrt{5})(\sqrt{6}-\sqrt{5} ) }-\dfrac{3\sqrt{2} (\sqrt{15}-3\sqrt{2} ) }{(\sqrt{15}+3\sqrt{2} )(\sqrt{15}-3\sqrt{2} ) }}$

$\sf{=\dfrac{7\sqrt{3} (\sqrt{10}-\sqrt{3} )}{10-3 }-\dfrac{2\sqrt{5}(\sqrt{6}-\sqrt{5} ) }{6-5 }-\dfrac{3\sqrt{2} (\sqrt{15}-3\sqrt{2} ) }{15-18 }}$

$\sf{=\dfrac{7\sqrt{3} (\sqrt{10}-\sqrt{3} )}{7 }-\dfrac{2\sqrt{5}(\sqrt{6}-\sqrt{5} ) }{1 }-\dfrac{3\sqrt{2} (\sqrt{15}-3\sqrt{2} ) }{-3 }}$

$\sf{=\sqrt{3} (\sqrt{10}-\sqrt{3} )-2\sqrt{5}(\sqrt{6}-\sqrt{5} ) +\sqrt{2} (\sqrt{15}-3\sqrt{2} ) }$

$\sf{=\sqrt{30}-3-2\sqrt{30}+10 +\sqrt{30}-6 }$

$\sf{=-3+10 -6 }$

$\sf{=1}$