Question

Rationalise the denominator:
3 / √3-√2+√5
solve that........​

Answer 1

did you mean

$\huge \pink{ \frac{3}{ \sqrt{3} - \sqrt{2} + \sqrt{5} } }$

Answer:

$\blue{\frac{3}{ \sqrt{3} - \sqrt{2} + \sqrt{5}}}\\ = \frac{3}{ \sqrt{3} - \sqrt{2} + \sqrt{5}} \times \orange{ \: \frac{\sqrt{3} + \sqrt{5} + \sqrt{2}}{\sqrt{3} + \sqrt{5} + \sqrt{2}} }\\ = \frac{3(\sqrt{3} + \sqrt{5} + \sqrt{2})}{ {(\sqrt{3} + \sqrt{5} )}^{2} - 2 } \\ = \frac{3 \sqrt{3} + 3 \sqrt{5} + 3 \sqrt{2} }{3 + 5 + 2 \sqrt{15} - 2} \\ = \frac{3 \sqrt{3} + 3 \sqrt{5} + 3 \sqrt{2} }{6+ 2 \sqrt{15} } \\ = \frac{3 \sqrt{3} + 3 \sqrt{5} + 3 \sqrt{2} }{6+ 2 \sqrt{15} } \times \green{\frac{6 - 2 \sqrt{15}}{6 - 2 \sqrt{15}}}\\ = \frac{(6 - 2 \sqrt{15})(3 \sqrt{3} + 3 \sqrt{5} + 3 \sqrt{2})}{36 + 60} \\ = \frac{18 \sqrt{3} +18 \sqrt{5} +18 \sqrt{2} - 6 \sqrt{5} - 6 \sqrt{3}- 6 \sqrt{30}}{96}$

$\huge \pink{Simplifying,\: we\: get}$

$= \huge {\green{\frac{2 \sqrt{3} +2 \sqrt{5} +3 \sqrt{2} - \sqrt{30}}{16}\:✓}}$

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Answer 2

Answer:

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