Question

prove that 5 minus root 3 is irrational given that root 3 is irrational​

Answer 1

Answer:

Hey dear here is your answer ^_^

⭐Let us assume that 5 - root 3 is rational. Then it can be written in the form

5 - root3 = p/q

or 5 - p/q = root3

It implies root3 is a rational number [Since 5 - p/q are rationals]

But this contradicts to the fact that root 3 is irrational. Hence our supposition was wrong. Therefore 5 - root 3 is irrational.

CHEERZ!

Hope it helped you out ⭐^_^⭐

Thanks ⭐(^^)⭐

Answer 2

Hello

Let us assume that 5 - √3 is rational.

Now, 5 - √3 = a/b where a and b are co primes

Now ,

$\sqrt{3} = \frac{5b - a}{b}$

Since a and b are integers √3 is rational...

But we know that √3 is irrational.. This situation arises because of our contrary assumption 5 - √3 is rational.

Therefore, 5 - √3 is irrational.. Hence Proved

Hope this helps you.......