Simplifying Radicals

Perfect Squares Perfect Cubes

Find the largest Perfect Square Factor LEAVE IN RADICAL FORM

This time Prime Factor the radicand LEAVE IN RADICAL FORM

and

To combine radicals: combine the ______________ of __________ radicals coefficients like

Simplify each expression

Simplify each expression: Simplify each radical first (largest perfect square) and then combine.

To multiply radicals: multiply the _____________ and then multiply the _____________. Simplify the remaining radicals. radicands coefficients

Multiply and then simplify

To divide radicals: divide the____________, if possible divide the __________, if possible _________________ the denominator so that no radical remains in the denominator radicands coefficients Rationalize

42 cannot be simplified, so we are finished. Rationalizing the denominator. This expression can not be divided which leaves a 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. Look back at slide #15

This can be divided, but this leaves a radical in the denominator. We do not 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. 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.