Question

rationalize the denominator and evaluated ​

Answer 1

Question :-

Rationalize the denominator √5/√5 - 1

Solution :-

When we rationalize the denominator we have to the denominator by changing the sign make fraction to multiple of given fraction and evaluate by using some identity.

Rationalization

$\sf:\longmapsto{ \frac{ \sqrt{5} }{ \sqrt{5} - 1} \times \frac{ \sqrt{5} + 1}{ \sqrt{5} + 1} } \\ \\ \sf:\longmapsto{ \frac{ \sqrt{5}( \sqrt{5} + 1) }{( \sqrt{5} ) {}^{2} - (1) {}^{2} } } \: \: \: \: \: \: \: \: \\ \\ \sf:\longmapsto{ \frac{5 + \sqrt{5} }{5 - 1} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bigstar\boxed{\sf:\longmapsto{} \frac{5 + \sqrt{5} }{4} } \: \: \: \: \: \: \: \:$

Additional information :-

Use some identity for the rationalization

• (a+b)² = a² + 2ab + b²
• (a-b)² = a² - 2ab + b²
• (a+b) (a-b) = a² - b²

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Answer 2

Answer:

$\frac{5 + \sqrt{5} }{6} \: is \: answer$

Step-by-step explanation:

$\sqrt{5 } \div \sqrt{5} - 1$

$\frac{ \sqrt{5} }{ \sqrt{5} - 1 } \times \frac{ \sqrt{5} + 1}{ \sqrt{5 } + 1}$

$\frac{5 + \sqrt{5} }{5 + 1?}$

$\frac{5 + \sqrt{5} }{6}$