Explanation:
V15 is rational ( contradiction method). V15=a/b (a and b are not common factor). squaring on both sides, we get, 15= a^2/b^2. 15b^2=a^2 (a=15c) b^2=15/a^2 (assume, a^2 =225c^2) 15b^2=225c^2 b^2=225c^2/15 b^2=15c^2 c^2=15/b^2 c =15/b. 15 divided both a and b which is a contradiction. ie, is irrational.