Q. 9: Given that v2 is irrational, prove tha: 5+3/2) is an irrational

1.	Q. 9: Given that v2 is irrational, prove tha: 5+3/2) is an irrational number.
Answer» We know √2 is irrational. Let 5 + 3 √2 be rational so, 5 + 3 √2 = r, where r is rational. √2 = (r - 5)/3 So, this is an absurd result because RHS is rational and RHS is irrational therefore a contradiction to our assumption. So, 5 + 3 √2 is irrational.

Q. 9: Given that v2 is irrational, prove tha: 5+3/2) is an irrational number.

Answer»

We know √2 is irrational.

Let 5 + 3 √2 be rational so,

5 + 3 √2 = r, where r is rational.

√2 = (r - 5)/3

So, this is an absurd result because RHS is rational and RHS is irrational therefore a contradiction to our assumption.

So, 5 + 3 √2 is irrational.