Answer :

since root3 is an irrational number 17root3 is also an irrational number 
a rational number + an irrational number =an irrational number 
so 15 +17root3 is an irrational number

Simple answer is √3 is irrational no.so when u add a rational no. to an irrational no. it will automatically give an irrational no. as the answer.