How do you simplify sqrt(80)80?

1 Answer
Jul 23, 2015

If a, b >= 0a,b0 then sqrt(ab) = sqrt(a)sqrt(b)ab=ab
If a >= 0a0 then sqrt(a^2) = aa2=a

Hence sqrt(80) = sqrt(16*5) = 4sqrt(5)80=165=45

Explanation:

sqrt(80) = sqrt(16*5) = sqrt(4^2*5) = sqrt(4^2)sqrt(5) = 4sqrt(5)80=165=425=425=45

Note that since sqrt(81) = sqrt(9^2) = 981=92=9 then

9/4 = sqrt(81)/(sqrt(80)/sqrt(5)) = sqrt(81/80)sqrt(5)94=81805=81805 is a useful approximation for sqrt(5)5.