Embed Code - If you would like this activity on your web page, copy the script below and paste it into your web page.

Normal Size Small Size show me how

Normal Size Small Size show me how

# Module 13

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

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

Simplify: √5 · √4y = | Answer: √20y To solve this problem we use the product rule. Product Rule: if n√a are real numbers n√b then n√a·n√b = n√ab |

Simplify: √21/25 = | Answer: √21/√25 For this problem we use the quotient rule. Quotient Rule: if if n√a are real numbers n√b and n√b ≠ 0 then n√a/b = n√a / n√b |

Simplify: √30/√5 = | Answer: √6 In solving this problem we use the quotient rule. These are the steps used to solve: 1.Place both numbers under the square root symbols √30/5 2. Then divide √30/5 which equals √6 |

Find the distance between the two coordinates: (5,2) and (9,6) | Answer: 4√2 We use the distance formula: √(x2-x1)²+(y2-y1)² Insert coordinates: √(9-5)²+(6-2)² Solve: √(9-5)²+(6-2)² = √(4)²+(4)² Simplify: √(4)²+(4)² = √32 Simplify: √32 = 4√2 |

Find the mid point of the two coordinates: (6,2) and (12,5) | Answer: (9,7/2) Here we use the mid point formula: ((x1+x2)/2 , (y1+y2)/2) Insert coordinates: ((6+12)/2 , (2+5)/2) Solve: ((6+12)/2 , (2+5)/2) = ((18)/2 , (7)/2) Simplify: ((18)/2 , (7)/2) = (9,7/2) |

Add the radicals: 2√50 + 5√32 = | Answer:34√2 You can add or subtract like radicals. Like radicals are where the indexes and the radicands are the same. Simplify: 2√50 + 5√32 = 2√25·√2 + 5√16·√2 Simplify:2√25·√2 + 5√16·√2= 14√2 + 20√2 Now you can add like radicands: 14√2 + 20√2 = 34√ |

Subtract the radicals: 5∛24-∛81 =? | Answer: 7∛3 You can add or subtract like radicals. Like radicals are where the indexes and the radicands are the same. Simplify: 5∛24-∛81 = 5∛8·∛3-∛27·∛3 Solve: 5∛8·∛3-∛27·∛3 = 10∛3-3∛3 Subtract: 10∛3-3∛3 = 7∛3 |

Multiply the radicals: (3√6+√7)(4√5-2√6)= | Answer:12√30-36+4√35-2√42 To solve we are going to either the distributive property or the FOIL method. FOIL: (3√6+√7)(4√5-2√6) Multiply: 12√6·√5-6√6·√6+4√5·√7-2√6·√7 Simplify:12√30-6·6+4√-2√42 Answer: 12√30-36+4√35-2√42 You can't simplify anymore. |

What is the distance formula? | The distance formula is √(x2-x1)²+(y2-y1)² |

What is the mid point formula? | The mid point formula is ((x1+x2)/2 , (y1+y2)/2) |

Created by:
byers.nathan