Question

answer the question above​

Answer 1

Answer:

13

Step-by-step explanation:

One of the method to solve this problem can be to rationalize the roots for the 3 terms separately.

$\frac{7 \sqrt{3} }{ \sqrt{10} + \sqrt{3} } \times \frac{\sqrt{10} - \sqrt{3} }{\sqrt{10} - \sqrt{3} } = \frac{7 \sqrt{30} - 21}{7} = \frac{7( \sqrt{30} - 3)}{7} = \sqrt{30} - 3$

$\frac{2 \sqrt{5} }{ \sqrt{6} + \sqrt{5} } \times \frac{ \sqrt{6} - \sqrt{5} }{ \sqrt{6 } - \sqrt{5} } = \frac{2 \sqrt{30 } - 10}{1} = 2( \sqrt{30} - 5)$

$\frac{3 \sqrt{2} }{ \sqrt{15} + 3 \sqrt{2} } \times \frac{ \sqrt{15} - 3 \sqrt{2} }{ \sqrt{15} - 3 \sqrt{2} } = \frac{3 \sqrt{30} - 18 }{ - 3} = \frac{3( \sqrt{30} - 6)}{ - 3} = - \sqrt{30} - 6 = - ( \sqrt{30} + 6)$

Substituting the simplified terms in the equation,

$( \sqrt{30} - 3) - 2(\sqrt{30} - 5) + (\sqrt{30} + 6) \\ = \sqrt{30} - 3 - 2 \sqrt{30} + 10 + \sqrt{30} + 6 \\ 2 \sqrt{30} - 2 \sqrt{30} + 13 = 13$

Answer 2

Answer:

13

Step-by-step explanation:

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