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# Module 13

### Simplifying, Adding, Subtracting, and Multiplying Radical Expressions

Question | Answer |
---|---|

What is a Radical Expression? | A radical expression: any expression containing a radical symbol. Many people mistakenly call this a 'square root' symbol. Though many times it's used to determine the square root of a number, it can also be used to describe a cube root, a 4th root etc. |

How do you simplify Radical Expressions? | Find the largest perfect square by dividing evenly into the no. under your radical, write the no. under your radical as the product of the perfect square & your answer from dividing. Give each no. its own radical sign and reduce the "perfect" radical. |

How to add/subtract Radicals: | To add/subtract radicals, begin by simplifying radicals, then combine like radicals, and add or subtract the radicals as needed. |

How to multiply Radical Expressions: | First, start with simplifying the radicals. Then, multiply the numbers outside the radicals followed by multiplying the numbers inside the radicals. |

How to divide Radical Expressions: | When dividing radicals start by simplifying each radical, then divide the numbers outside the radicals followed by dividing the numbers inside the radicals. |

True or false? Both the product and quotient rules can be used to simplify a radical. | True |

Multiply the square root of 2 times the square root of 3x. | Since both indexes are the same, you end up with the square root of 2 * 3x. You can now simplify by multiplying. 2 * 3x = 6x Your answer is the square root of 6x. |

The quotient rule for radicals | The inth root of the quotient of a over b, is equal to the inth root of a over the inth root of b. |

Use the quotient rule to simplify the square root of 25 over 49. | Start by separating the radicals so it becomes square root of 25 ofer the square root of 49. Then, since both numbers are perfect squares, you may simplify. Square root of 25 = 5, and the square root of 49 = 7. Your answer simplifies and becomes 5/7. |

Use the quotient rule to simplify the square root of 75 over the square root of 3. | Since there is a common factor of 3, use the quotient rule and write it as the square root of 75/3. This puts them under the same radical sign so you may divide. 75/3 = 25 Finish by simplifying. The square root of 25 = 5 |

Created by:
Mary.lesniak