Question

rationalize the denominator √5/5+√5​

Answer 1

Answer:

5 root 5 - 25 / 20

Step-by-step explanation:

root 5 / 5+ root 5 * 5-root 5/5-root5

root 5 * 5-root 5/5+root 5*5-root 5

5 root 5 -25 / 20

Answer 2

Answer $= \frac{\sqrt{5} - 1 }{4}$

Explanation:

To rationalize:    $\frac{ \sqrt{5} }{5 +\sqrt{5} }$

Proof:

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

Multiplying both numerator and denominator by ( 5 - √5 )

$=\frac{ \sqrt{5} }{5 +\sqrt{5} } X \frac{5 -\sqrt{5}}{5 -\sqrt{5}}$

$=\frac{ \sqrt{5} (5 - \sqrt{5})}{(5 +\sqrt{5}) ( 5 - \sqrt{5})}$

$= \frac{5\sqrt{5} - 5 }{5^2 - (\sqrt{5})^2 }$                                                [ (a - b )² = a² - b² ]

$= \frac{5(\sqrt{5} - 1) }{25 - 5 }$

$= \frac{5(\sqrt{5} - 1) }{20}$

$= \frac{\sqrt{5} - 1 }{4}$

Hence, proved.

Hope you got that.

Thank You.