Question

prove that root 3 + root 5 is an irrational number​

Answer 1

Answer:

let say that it be a rational number and it have to primes as a and b which can be expressed as a/b

Step-by-step explanation:

$\sqrt{3} + \sqrt{5} = \frac{a}{b}$

$3 + 2 \sqrt{3} \sqrt{5} + 5 = \frac{ {a}^{2} }{ {b}^{2} }$

$2 \sqrt{5} \sqrt{3} = \frac{ {a}^{2} }{ {b}^{2} } - 8$

$\sqrt{3} = \frac{ {a}^{2} - 8 {b}^{2} }{2 \sqrt{5} {b}^{2} }$

so, a and b are integers so Rhs is rational and so lhs be also rational .

but √3 is irrational .

So our contradict is wrong that we assume that √3+√5 is rational .

so √3+√5 is irrational.