How do you simplify square roots? - Answers

Make use of the property that sqrt(ab)=sqrt(a) x sqrt(b) and try to find an 'a' or 'b' that can be expressed as a whole number; these combinations of a square root and a coefficient are called surds.e.g. In square root form, sqrt(18) = sqrt(9 x 2)= sqrt(9) x sqrt(2). This, in surd form, is 3 x sqrt(2).Note that the property sqrt(ab) = sqrt(a) X sqrt(b) does not hold for negative radicands (imaginary numbers) unless negative roots are accounted for. For example, it is known that sqrt(-1) X sqrt(-1) = -1. The property mentioned above would imply that sqrt(-1) X sqrt(-1) = sqrt(-1 X (-1) = sqrt(1) which is only true if the square root of 1 is taken to be either 1 or -1.