Question 390827
75 in factored form is {{{5^2 * 3}}}. Therefore, {{{sqrt(75) = sqrt(5^2 * 3)}}}. Since {{{sqrt(ab) = sqrt(a)sqrt(b)}}} for real numbers a,b (not complex numbers), then {{{sqrt(5^2 * 3) = sqrt(5^2)sqrt(3) = 5sqrt(3)}}}.


It doesn't necessarily work for complex numbers because


{{{sqrt(-1)sqrt(-1) = i*i = -1}}} and if {{{sqrt(-1)sqrt(-1) = sqrt((-1)(-1)) = sqrt(1) = 1}}}, then -1 = 1 and we have a contradiction.