Question

7√3/10+√3 - 2√5/√6+√5 - 3√2/√15+3√2 simplify​

Answer 1

Step-by-step explanation:

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,

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

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

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

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

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

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

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

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

$⟹ \cancel{2 \sqrt{30} } - 9 - \cancel{2 \sqrt{30} } + 10$

$⟹ - 9 + 10$

$⟹9 - 10$

$⟹1 \: \: \: \: Ans.$

# Learn more:

Rationalize the denominator.

i. 1/(√7 + √2)

ii. 3/(2√5 - 3√2)

iii. 4/(7 + 4√3)

iv. (√5 - √3)/(√5 + √3)

https://brainly.in/question/2846541