Simplifying Radicals

Perfect Squares 64 225 1 81 256 4 100 289 9 121 16 324 144 25 400 169 36 196 49 625

Simplify = 2 = 4 = 5 This is a piece of cake! = 10 = 12

Simplify = = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM = = = = = =

Simplify = = = = = = = = = = Perfect Square Factor * Other Factor LEAVE IN RADICAL FORM = = = = = =

Multiplying Radicals × To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals. Outside × Outside / Inside × Inside

Multiply and then simplify  

Dividing Radicals To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains in the denominator

That was easy!

42 cannot be simplified, so we are finished. This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator. 42 cannot be simplified, so we are finished.

This can be divided which leaves the radical in the denominator This can be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.  

This cannot be divided which leaves the radical in the denominator This cannot be divided which leaves the radical in the denominator. We do not leave radicals in the denominator. So we need to rationalize by multiplying the fraction by something so we can eliminate the radical in the denominator.   Reduce the fraction.