Question

rationalize between 1/2+£5

Answer 1

Hi friend, Harish here.

Here is your answer:

To Rationalize: 

$\frac{1}{2+ \sqrt{5} }$

Solution,

To rationalize the denominator, We must multiply and divide the number by it's conjugate.

Conjugate of the denominator  = 2 - √5.

Then,

$\frac{1}{2+ \sqrt{5} } \times \frac{2- \sqrt{5} }{2- \sqrt{5} }$

⇒ $\frac{2- \sqrt{5} }{(2+ \sqrt{5})(2- \sqrt{5}) } = \frac{2- \sqrt{5} }{4-5} = \frac{2- \sqrt{5} }{-1}= - (2- \sqrt{5}) = \sqrt{5}-2$

Here we used the identity (a+b)(a-b) = a² - b² while multiplying in the denominator.

(That is (2+√5)(2-√5) = 2² - (√5)² = 4 - 5 = -1)

Therefore the rationalized number is √5 - 2.
__________________________________________________

Hope my answer is helpful to you.

Answer 2

i am considering the question as

1/(2+√5)

1/(2+√5) = 1/(2+✓5) * (2-✓5)/(2-√5)

=(2-√5)/(4-5)
=(2-√5)/-1
=(√5-2)/1
=√5 - 2

i hope it helps....