Question

if √5 is an irrational number then prove that 3+√5 is an irrational
numbers​

Answer 1

Answer:

Let us assume that 3+√5 is a rational number.

Now,

3+√5=a/b [Here a and b are co-prime numbers]

√5 =[( a/b)−3]

√5=[(a−3b)/b]

Here, [( a−3b)/b] is a rational number.

But we know that √5 is an irrational number.

So, [( a−3b)/b )] is also a irrational number.

So, our assumption is wrong.

3+√5 is an irrational number.

Hence, proved.