Question

(2) Prove that 3+root 5 is an irrational number.... ​

Answer 1

Step-by-step explanation:

Let us assume that 3+

5

is a rational number.

Now,

3+

5

=

b

a

[Here a and b are co-prime numbers]

5

=[(

b

a

)−3]

5

=[(

b

a−3b

)]

Here, [(

b

a−3b

)] is a rational number.

But we know that

5

is an irrational number.

So, [(

b

a−3b

)] is also a irrational number.

So, our assumption is wrong.

3+

5

is an irrational number.

Hence, proved.

Answer 2

Answer:

let us suppose 3+root 5 is rational. as p, q and 3 are integers p-3q/3 is a rational number. =>root 5 is a rational number. ... hence 3+ root 5 is an irrational number.