Simplifying All Kinds of Radicals Unit 7 Simplifying

Simplifying All Kinds of Radicals Unit 7 – Simplifying Radicals

Simplifying Square Roots � Simplify � If the number is not a perfect square, find a factor that is a perfect square: 4 times 6 � Take the square root of the perfect square � � If you have an even exponent, you take half of the exponent when you take the square root. � This is the simplified answer! � Simplify � If the number is not a perfect square, find a factor that is a perfect square: 16 times 3 � Take the square root of the perfect square � � If you have an odd exponent, you take split the exponent by one and whatever is left over, which is even. � �

Simplifying Cube Roots �Simplify �If the number is not a perfect cube, find a factor that is a perfect cube: 8 times 3 � Take the cube root of the perfect cube � �If you have an exponent that is a multiple of 3, you divide the exponent by 3 when you take the cube root � This is the simplified answer! Simplify • If the number is not a perfect cube, find a factor that is a perfect cube: 125 times 2 • Take the cube root of the perfect cube • • If you have an exponent that is not a multiple of 3, you find the closest multiple of three, • This is the simplified answer! •

Rationalizing a Denominator with a Square Root �You cannot leave a radical in the denominator of any fraction. �You must create a perfect square in the denominator so that you can take the square root of that number and the radical disappears. �You must multiply the numerator and the denominator by the same thing.

Rationalizing a Denominator with a Square Root �Example - Simplify: �We have to turn the into a perfect square to that means we have to multiply by. �Multiply �Final answer No more radical in the denominator!

Rationalizing a Denominator with a Cube Root or Fourth Root �You cannot leave a radical in the denominator of any fraction. �You must create a perfect cube in the denominator so that you can take the cube root of that number and the radical disappears. �You must multiply the numerator and the denominator by the same thing.

Rationalizing a Denominator with a Cube Root or Fourth Root �Example - Simplify: �We have to turn the into a perfect cube to that means we have to multiply by. �Multiply �Final answer No more radical in the denominator!

Adding and Subtracting Radical Expressions �In order to add or subtract radical expressions, they must be like terms. �Like terms for radicals include the following: the same root and the same number/term inside the radical. �You simply add the coefficients (numbers in front of radical) together. �The numbers inside the radicals do not get added together! �If both of those things are not the same, then you cannot add or subtract them!

Adding and Subtracting Radical Expressions Radicals with Like Terms Radicals with Non-like Terms �Example �The number inside the radical is 3 each time so just add/subtract the coefficients �Final answer �Example �You cannot do anything to this one because the number s inside the radical are all different

Adding and Subtracting Radical Expressions �Sometimes you have to simplify first before adding or subtracting �Example �Simplify each radical first �Now combine like terms, if possible

Multiplying and Dividing Radical Expressions �You can multiply or divide anything as long as the radical expression has the same root! �The numbers on the outside are multiplied together. �The numbers on the inside of the radical are multiplied together. �Now simplify!

Multiplying and Dividing Radical Expressions Multiplication Division �Example �Multiply �Divide �Simplify

Rationalizing a Denominator with a Binomial Including a Radical �We have already talked about these kinds of problems. �You must multiply the numerator and denominator by the conjugate of the denominator! �That will divide out the radical and leave you with an integer.

Rationalizing a Denominator with a Binomial Including a Radical �Example �Multiply by the conjugate �Multiply �Simplify