Question

If root 3 is irrational . Prove that 5+2 root 3 /7 is also irrational.

Answer 1

Let us assume that 5+2root3/7 is a rational number

then

5+2root3/7=a/b(where a,b are integers and b not equal to zero)

5+2root3/7=a/b

5+2root3=a/7b

2root3=(a/7b)-5

2root3=(a-35b)/7b

root3=(a-35b)/14b

a, b,13 and 14 are integers. But root3 is an irrational number.

So, our assumption is wrong.

5+2root3 is an irrational number.