Multiplying & Dividing Radical Expressions

Gm1m2 r2 The formula F = relates the gravitational force F between an object of mass m1 and an object of mass m2 separated by a distance r. G is a constant known as the constant of gravitation. Solve the formula for r. To accomplish this, we need to know how to multiply and divide with radicals.

Property: In other words, a radical times another radical is a bigger radical.

Examples: Simplify if possible.

The radicals must have the same index to do this. Examples: The radicals must have the same index to do this. Simplify if possible.

Examples: We cannot multiply these at the moment…they do not have the same index.

Examples: The property for multiplying radicals does not apply here since -4 is not a real number.

Group Numbers and like variables. Simplifying Radical Expressions: Now split apart the variables into powers that are multiples of the index. Simplify the numbers. Group Numbers and like variables.

Simplifying Radical Expressions:

Simplifying Radical Expressions:

Your Turn: = = =  =

Property: In other words, a radical divided by another radical is a smaller radical.

The radicals must have the same index to do this. Examples: The radicals must have the same index to do this. =

Examples: = = = = = =

Your Turn: = = =

Basic Rules of Radicals: You can’t leave a perfect nth power factor under the radical. You can’t leave a fraction under a radical (this includes decimals). You can’t leave a radical in the denominator of a fraction.

You must RATIONALIZE denominators. We call clearing a denominator of radicals RATIONALIZATION. You must RATIONALIZE denominators. RATIONALIZE by turning the denominator into a perfect power.

Place the expressions under one radical. Examples: = = = Simplify. Place the expressions under one radical.

= = =  = = Examples: Place the expressions under one radical. You can’t leave a fraction under the radical. Simplify. Rationalize…Turn the denominator into a perfect square. =

Examples: = = = =  = = =

Examples: = = = =  = = =

Examples: = = = = = =

 = = =

The volume of a sphere of radius r is: Use the formula to find r in terms of V. Rationalize the denominator. Use your answer above to find the radius of a sphere with volume 100 in3. Round to the nearest hundredth.