Question

show that 5-√3 is an irrational no. given that √3 is irrational.
​

Answer 1

Step-by-step explanation:

Let us assume that 5-√3 is rational number so we can find two integers a and b. Where a and b are two co - primes number and b≠0

= 5-√3 = a/b

= √3= 5- a/b

=> a and b are integers so (5 - a/b ) is rational

But √3 is irrational ( we know that and it is given)

This problem has arise due to our wrong assumption that 5 - √3 is rational number.

Hence, 5 -√3 is irrational number.

Hope it helps you