Question

rationalise the denominator 3/4√5-√3+2/4√5+√7

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Answer 1

$\huge\mathtt\red{answer : - }$

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$\to \: {\mathtt{\frac{3}{4} \sqrt{5} - \sqrt{ \frac{3 + 2}{4} } \sqrt{5} + \sqrt{7} }}$

$\to {\mathtt{ \frac{3}{4} \sqrt{5} - \sqrt{ \frac{5}{4}} \sqrt{5} + \sqrt{7} }}$

$\to \: \mathtt{ \frac{3}{4} \sqrt{5} - \frac{ \sqrt{ 5}}{ \sqrt{4} } \sqrt{5} + \sqrt{7} }$

$\to \mathtt{ \frac{3}{4} \sqrt{5} - \frac{ \sqrt{5} }{2} \sqrt{5} + \sqrt{7} }$

$\to \mathtt{ \frac{3}{4} \sqrt{5} - \frac{ \sqrt{5} \sqrt{5} }{5} } + \sqrt{7}$

$\to \mathtt \red{ \frac{3}{4} \sqrt{5} - \frac{5}{2} \sqrt{7} }$

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Therefore:-

$\to \mathtt \red{ \frac{3}{4} \sqrt{5} - \frac{5}{2} \sqrt{7} }$

Answer 2

Answer:

→435−43+25+7

$\to {\mathtt{ \frac{3}{4} \sqrt{5} - \sqrt{ \frac{5}{4}} \sqrt{5} + \sqrt{7} }}→435−455+7</p><p>\to \: \mathtt{ \frac{3}{4} \sqrt{5} - \frac{ \sqrt{ 5}}{ \sqrt{4} } \sqrt{5} + \sqrt{7} }→435−455+7</p><p>\to \mathtt{ \frac{3}{4} \sqrt{5} - \frac{ \sqrt{5} }{2} \sqrt{5} + \sqrt{7} }→435−255+7</p><p>\to \mathtt{ \frac{3}{4} \sqrt{5} - \frac{ \sqrt{5} \sqrt{5} }{5} } + \sqrt{7}→435−555+7</p><p>\to \mathtt \red{ \frac{3}{4} \sqrt{5} - \frac{5}{2} \sqrt{7} }→43$

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Therefore:-

\to \mathtt \red{ \frac{3}{4} \sqrt{5} - \frac{5}{2} \sqrt{7} }→435−257