How do you simplify #sqrt(37-4sqrt(75))# ?
1 Answer
Jan 16, 2018
Explanation:
I think you mean the positive square root of
Note that:
#37-4sqrt(75) = 37-4sqrt(5^2*3)#
#color(white)(37-4sqrt(75)) = 37-20sqrt(3)#
#color(white)(37-4sqrt(75)) = 5^2-2(5)(2sqrt(3))+3*2^2#
#color(white)(37-4sqrt(75)) = (5-2sqrt(3))^2#
Also note that
So:
#sqrt(37-4sqrt(75)) = 5-2sqrt(3)#
