Question

rationalize
3. 3/2-√5​

Answer 1

Step-by-step explanation:

here is ur answer hope it helps uh

Answer 2

Given to rationalize the denominator :-

$\dfrac{3}{2-\sqrt{5} }$

SOLUTION :-

Since, we need to rationalize the denominator means we have to multiply with the numerator and denominator with its conjugate.

The conjugate of denominator of $2-\sqrt{5} \: is \: 2+\sqrt{5}$

So, multiply with the numerator and denominator

$\dfrac{3}{2-\sqrt{5} } \times \dfrac{2+\sqrt{5} }{2+\sqrt{5} }$

$\dfrac{3(2+\sqrt{5}) }{(2+\sqrt{5})(2-\sqrt{5}) }$

Solving the denominator by using algebraic identity (a+b)(a-b) = a²-b²

$\dfrac{6+2\sqrt{5} }{(2)^2-(\sqrt{5} )^2}$

$\dfrac{6+2\sqrt{5} }{4-5}$

$\dfrac{6+2\sqrt{5} }{-1}$$-(6+2\sqrt{5} )$

$(-6-2\sqrt{5} )\div 1$

Since , the denominator rationalized !!

Rationalization means :- The surds of a denominator must be removed by the process of rationalization .