1. DIVIDING RADICALS

2. DIVIDING RADICALS – THE BASICS Like with multiplying radicals, to divide radicals they must have the same INDEX. Remember, division is often written as a fraction. As with multiplying radicals, you can divide/reduce the coefficients to get the coefficient of the quotient, then divide/reduce the radicand to get the radicand of the quotient. The final basic fact you need to know is: to take the root of a fraction, you take the root of both the numerator and denominator. Lets try some examples…

3. Are the indices the same? YEP!!! Let’s do this! Divide/reduce the coefficients and radicands. Simplify your radical Are the indices the same? YEP!!! Let’s do this! Divide/reduce the coefficients and radicands. Simplify your radical. What happened to the denominator? Divide num. & denom. by 3 Divide num. & denom. by 25 Divide num. & denom. by 2 Final check: are your radical and fraction completely simplified?

4. How do I take the square root of a fraction? Take the square root of the numerator and denominator separately. But make your life easier – simplify your fraction first. Now split it up and simplify. Since the radicand is a fraction, simplify the fraction first. Take the root of the denom. and numerator separately. Simplify. How do you divide powers? Where does the -6 go?? Nope, we’re not done yet. One more small step for man, one giant leap for fraction kind.. Divide num. & denom. by 7 Divide num. & denom. by 3

5. ONE OF THOSE REALLY IMPORTANT MATH RULES…. You know you need to simplify fractions completely, combine like terms, simplify radicand, etc. before you can say you have ‘finished’ a problem. One other rule you need to know is that you NEVER leave a radical in the denominator of a fraction! We will use our knowledge of simplifying radicals and of equivalent fractions to make sure we don’t break this rule!

6. RATIONALIZING DENOMINATORS Step 1 – simplify our fraction Step 2 – simplify our radicands Step 3 – rationalize the denominator Why do we still have a radical in the denominator? What would we need for the radical to simplify? Final check: are your radical and fraction completely simplified?

7. RATIONALIZING DENOMINATORS Step 1 – simplify the fraction Step 2 – split it up and simplify the radicands Step 3 – rationalize the denominator Why do we still have a radical in the denominator? What would we need for the radical to simplify? Final check: are your radical and fraction completely simplified?

8. RATIONALIZING THE DENOMINATOR