Question

Prove that: 3- $\sqrt{5}$ is an irrational number, given that
$\sqrt{5}$ is an irrational number.

Answer 1

Answer:

Prove that: 3- $\sqrt{5}$ is an irrational number, given that

Prove that: 3- $\sqrt{5}$ is an irrational number, given that$\sqrt{5}$ is an irrational number.

Answer 2

Root3 is an irrational number.

Solution:

(Were p and q is a co-prime)

Squaring both the side in above equation

if 3 is a factor of

Then, 3 will also be a factor of p

{where m is a integer}

Squaring both sides we get

Substitute the value of  in the equation

If 3 is a factor of

Then, 3 will also be factor of q

Hence, 3 is a factor of p & q both

So, our assumption that p & q are co-prime is wrong.

So,  is an "irrational number". Hence proved.