Question

show that 3+root 5is irrational
​

Answer 1

Answer:

I think it helps you ⬇⬇

Step-by-step explanation:

Let us assume that 3+√5 is rational by conctradiction.

$3+\sqrt{5}=\frac{a}{b}[Where\:a\:and\:b\:are\:co-primes\:and\:b\neq 0]$

     $\sqrt{5}=\frac{a}{b}-3$

     $\sqrt{5}=\frac{a-3b}{b}$

As,$\frac{a-3b}{b}$ is rational,√5 is also a rational number.

But we know that √5 is irrational.

So,this contradiction has arisen because of our  incorrect assumption that 3+√5 is rational.

∴3+√5 is rational.

Please mark it as brainlist answer