Question

rationalise the denominator ​

Answer 1

Answer:

1.

Step-by-step explanation:

Given that:

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

What to do:

To simplify

Solution:

We have,

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

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

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

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

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

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

$⟹ \tt{ - 9 + 10}$

$⟹ \tt{1 \: \: ans.}$

Answer 2

1 is the answer of your question