d=√(〖(√7-(-√2))〗^2+〖((-√2)-√(5))〗^2))

Question

This is for my College Algebra class. It is a distance problem. I would like step by step instrustion on getting the answer. I have found many sites that will just give me the correct answer, but it is not helping me because it doesn't show me what I need to do to get that anwer

Answer 1

d=√{[(√7-(-√2))]²+[((-√2)-√(5))]²}.

Work out the two squared terms first:

[(√7-(-√2))]²=[(√7+√2)]²=[9+2√14];

[((-√2)-√(5))]²=[(-√2-√5)]²=[√2+√5]²=[7+2√10];

d=√{16+2√10+2√14}=√{16+6.3246+7.4833};

d=√29.8079=5.4597 approx.