Question

√5 + √7 show it as a irrational number ?

Answer 1

Let 5+√7 be a rational number 
Now 5+√7=a/b 
a/b-5=√7 
a-5b/b=√7. 
Now if p is a +ve prime then √p is irrational. 
Therefore √7 is irrational. 
Hence, 5+√7 is an irrational number.