Question

Prove that root3 + root5 is irrational? ​

Answer 1

$\sqrt{3} + \sqrt{5} \: is \: an \: irrational \: number$

This is because neither of them is negative and cannot cancel each other out. But sometimes, the sum of 2 irrational numbers can be rational too.

For example,

$(2 + \sqrt{3} )$

It is an irrational number.

$(2 - \sqrt{3} )$

It is also an irrational number.

But if you add both of them:-

$(2 + \sqrt{3} ) + (2 - \sqrt{3} ) \\ = 2 + \sqrt{3} + 2 - \sqrt{3} \\ = 4 \\ ( \sqrt{3} \: and \: - \sqrt{3} \: cancel \: each \: other)$

So sum of 2 irrationals can be either irrational or rational. But sum of sqrt 2 and sqrt 5 is irrational.

Answer 2

root3 + root5

is irrational because root 3 is 1/2 of 3 and,If you divide it further it's quotient will be a non-terminating number.

similarly,root 5 is a irrational number too

Step-by-step explanation:

if you add them

root 5+root 3 = 5 1/2 + 3 1/2

=8 1/2

if you take lowest common factor

2.2.2

if you take a pair it will be

2 root 2

which is irrartional.