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# RADICAL EXPRESSIONS

### SIMPLIFYING, ADDING, SUBTRACTING, AND MULTIPLYING

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

Use the product rule to multiply ∜2x^2y × ∜5xy | ∜(2x^2y)(5xy)= ∜10x^3y^2 Note that both radicals have an index number of 4, so you can put their product together under one radical keeping the 4 as its index number. |

Use the quotient rule to simplify ∛5/8 | Use the quotient rule of radicals to rewrite as ∛5/∛8 then simplify ∛5/2 (We cannot take the cube root of 5, this is as simplified as it gets). |

Simplify -∛81a^5b^4 | Even though 81a^5b^4 is not a perfect cube, it does have a factor that we can take the cube root of. -∛(27a^3b^3)(3a^2b)= -3ab^3∛3a^2b |

Find the distance between the two points (8,-2) and (3, 9). | Use d=√(change in x)^2+(change in y)^2. √(8-3)^2+(-2-9)^2 =√25+121 = √146 = 12.08 |

Find the midpoint between (−9,−1) and (−3,7). | Use M= ((x_1+ x_2)/2),(y_1+ y_2)/2)). ((-9+(-3))/2),(-1+ 7)/2))= ((-12)/2, 6/2)= (-6,3) |

Add 2√20x + 3√5x | First, simplify the first radical expression: 2√20x = 2√(4)(5x)= 2(2)√5x = 4√5x. The second radical is already is simplest form. 2√20x + 3√5x = 4√5x + 3√5x = 7√5x |

Subtract (∜16x)/5 - (3∜x)/5 | Take the fourth root of the 16 in the first radical: (2∜x)/5. (2∜x)/5 - (3∜x)/5 = (-∜x)/5 |

Add or subtract ∛3b^3 -3b^3∛24 +2∛81b^3 | b∛3 -6b∛3 +6b∛3= b∛3 |

Multiply and simplify. Assume variable is positive. (√a -5)(3√a +7) | FOIL: 3√a^2 +7√a -15√a -35 and simplify: = 3a-8√a -35 |

Multiply. (√a+√b)(√a-√b) | a-b |

Created by:
amccausland