Question

rationalise (3-√5) ÷√5​

Answer 1

Answer:

Given,

Rationalise :-

$\frac{3 - \sqrt{5} }{\sqrt{5} }$

Let's Understand :-

to Rationalise the given number we need to multiply and divide the given number with $\sf\sqrt{5}$ . So that it does not changes the value of the given number.

Solution:-

$= \frac{3 - \sqrt{5} }{\sqrt{5} }$

$= \frac{3 - \sqrt{5} }{\sqrt{5} } \times \frac{\sqrt{5} }{\sqrt{5} }$

Multiplying both Numerators and Denominators Together :

$= \frac{(3 - \sqrt{5})\times\sqrt{5} }{\sqrt{5} \times \sqrt{5} }$

$= \frac{3\times(\sqrt{5})-(\sqrt{5} \times \sqrt{5)} }{5}$

$\sf\therefore\sqrt{5}\times \sqrt{5} = 5$

$= \frac{3\sqrt{5}-5 }{5}$

$\sf\therefore\sqrt{5}\times \sqrt{5} = 5$

$\frac{3 - \sqrt{5} }{\sqrt{5} }$ = $= \frac{3\sqrt{5}-5 }{5}$