Question

Prove that 5 root 7+3 root 2 is an irrational number

Answer 1

5$\sqrt{7}$+3$\sqrt{2}$ are irrational numbers
But think they are rational number.So we can write it in the form of p/q
5$\sqrt{7}$ +3$\sqrt{2}$=a/b(where a,b are co primes)
5$\sqrt{7}$+3$\sqrt{2}$=a/b
send 5 root 7 to the right side
then we get
3 root 2=a/b-5 root 7
3=a-5 root b/root 2 b
Above we can see that 3 is rational but on the right side they are irrational
so our assumption is wrong
5 root 7+3 root 2 is irrational number