Math, asked by theanswerguru, 2 months ago

Please answer asap.

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Answers

Answered by Salmonpanna2022

Given:-

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

What to do:-

Simplify

Solution:-

Let's solve the problem

we have,

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

$⟹ \frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } \times \frac{ \sqrt{10} - \sqrt{3} }{ \sqrt{10} - \sqrt{3} } - \frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} } \times \frac{ \sqrt{6} - \sqrt{5} }{ \sqrt{6} - \sqrt{5} } - \frac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} } \times \frac{ \sqrt{15} - 3 \sqrt{2} }{ \sqrt{15} - 3 \sqrt{2} } \\ \\$

$⟹ \frac{7 \sqrt{3}( \sqrt{10} - \sqrt{3} ) }{( \sqrt{10} + \sqrt{3} )( \sqrt{10} - \sqrt{3}) } - \frac{2 \sqrt{5}( \sqrt{6} - \sqrt{5} )}{( \sqrt{6} + \sqrt{5} )( \sqrt{6} - \sqrt{5}) } - \frac{3 \sqrt{2}( \sqrt{15} - 3 \sqrt{2}) }{( \sqrt{15} + 3 \sqrt{2})( \sqrt{15} - 3 \sqrt{2}) } \\ \\$

$⟹ \frac{7 \sqrt{3}( \sqrt{10} - \sqrt{3} )}{( \sqrt{10} {)}^{2} ( \sqrt{3} {)}^{2} } - \frac{2 \sqrt{5}( \sqrt{6} - \sqrt{5} ) }{( \sqrt{6} {)}^{2} - ( \sqrt{5} {)}^{2} } - \frac{3 \sqrt{2}( \sqrt{15} - 3 \sqrt{2} ) }{( \sqrt{15} {)}^{2} - (3 \sqrt{2} {)}^{2} } \\ \\$

$⟹ \frac{7 \sqrt{3}( \sqrt{10} - \sqrt{3} )}{10 - 3 } - \frac{2 \sqrt{5}( \sqrt{6} - \sqrt{5} ) }{6 - 5}-\frac{3 \sqrt{2}( \sqrt{15} - 3 \sqrt{2} ) }{15 - 18} \\ \\$

$⟹ \frac{ \cancel{7} \sqrt{3}( \sqrt{10} - \sqrt{3} )}{ \cancel{7 }} - \frac{2 \sqrt{5}( \sqrt{6} - \sqrt{5} ) }{1}-\frac{{ \cancel{3}} \sqrt{2}( \sqrt{15} - {3} \sqrt{2} ) }{ \cancel{3}} \\ \\$