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# Radical Expressions!

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

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

Use the product rule for radicals to find the following product. √7 times √6 | Combine both radicals under one radical sign using the product rule = √7*6 then simplify under the radical √42. Therefore, the anwser is √42 |

Use the quotient rule for radicals to solve √6/49 | Once quotient rule is applied you should have √6/√49. Simplify the denominator from √49 to 7. Combine to reach final anwser of √6/7. |

Use the product rule to multiply. ^3√4 times ^3√2 | Apply the product rule and rewite the expression. ^3√4*2 then multiply, which would equal = ^3√8. Simplify to reach your final anwser of 2. |

Use the quotient rule to simplify. ^3√x/64 | Apply rule to get ^3√x/^3√64. Simplify the denominator to 4. Combine anwsers to obtain final anwser of ^3√x/4. |

Simplify. 4√48 | Rewrite 48 as a product whose factor is a perfect square and apply product rule. =4 times √16 times √3. Simplify to obtain final anwser of 16√3. |

Simplify √9x^5 | Factor so that one factor is a perfect square. =(9x^4)(x). Then use the product rule to simplify √9x^4 √x. Simplify the first factor of the expression to get 3x^2√x as your final anwser. |

Find the distance between the pair of points. (-9,7) and (-3,6) | Put your numbers into the distance formula, then simplify to = √(6)^2+(-1)^2. Square it to get √36+1. Add to get √37, which means the distance is √37 units. Find exact distance and round to obtain final anwser of 6.083 units. |

Find the midpoint of the line segment (-5,-1) and (-3,6). | Subsitute known values into the midpoint fomula and Add! You will get =(-8/2, 5/2). Divide what you can to obtain (-4, 5/2) which is the final anwser. |

Find the midpoint of the line segment. (-13/16, 12/13) and (11/16, 14/13). | Subsitute values into the midpoint formula and add the numerators. =(-2/16/2,26/13/2) Then divide both fractions bby 2, and multiply by 1/2. =(-2/32,26/26) Simplify to reach final anwser of (-1/6,1) |

Add. 3√13/10 + 5√13/11. | Find the LCD of the fractions (110). Write each expression as an equivalent expression with denominator of 110. Multiply factors in the num. and den. =33√13/110 + 50√13/110. Add like fractions and simplify. 83√13/110 is the final anwser. |

Subtract. √28 - √175 | Factor the first radicand so its a perfect square. 28=4(7). Use product rule to simplify the first term. =(2)√7. Repeat for the second radicand. 175=25(7) and simplify, =(5)√7. Combine like radicals and obtain final anwser of -3√7. |

Multiply, then simplify. | Use (a-b)^2 as the formula. Plug in known values to get (√5)^2-2 times √5 times √6+(√6)^2. Square and use the product rule to simplify. =5-2√30 +6. Add like terms and obtain final anwser of 11-2√30. |

Created by:
Kimshankle1