Question

Prove that 3 + quare root of 5 is irrtional

Answer 1

3+ 25 =28 and it is irritinoal as it is not square of any no.

Answer 2

Step-by-step explanation:

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.