Question

Prove that 5 - √3 is an irrational number.
Please Reply quickly........​

Answer 1

Solution:-

Let us assume , to the contrary, that ( 5- √3 ) is rational

Then , there exist co-prime a and b ( b ≠ 0 )

( 5 - √3) = a / b

=> - √3 = a/b -5

=> - √3 =( a - 5b )/b

Since a and b are integers, so ( a - 5b )/b is rational

Thus √3 is also rational

But this contradicts the fact that √3 is irrational so our assumption is incorrect

Hence ( 5 - √3) is irrational

Definition of irrational number

=> The number which when expressed in decimal from are expressible as non terminating and non repeating decimals are know as irrational number