Question

prove that ✓3+✓5 is irrational​

Answer 1

Step-by-step explanation:

Method 1 -

Let

$\sqrt{3} + \sqrt{5} = x = rational\\Thus, \sqrt{3} = x - \sqrt{5} = rational$

But

$\sqrt{3} = Irrational$

Hence Proved,

$\sqrt{3} + \sqrt{5} = irrational$

Method 2 -

$\\\sqrt{3} + \sqrt{5} = x\ = rational \\\ Thus , (\sqrt{3} + \sqrt{5} )^{2} = x^{2} = rational\\=> 8 + 2\sqrt{15} =x^{2} = rational \\=> \sqrt{15} = \frac{x^{2} -8 }{2} = rational$

But

$\sqrt{15} = irrational$

Thus this is a contradiction .

Hence proved ,

$\sqrt{3} + \sqrt{5} = irrational$