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# Module 11

### Radicals and Radical Functions

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

Find the Square root. √576 | The positive square root of 576 is 24 because 24*24=576. |

Simplify : √(1/9) | √1/√9. √1 is 1 because 1*1=1; √9 is 3 because 3*3=9. And the answer is 1/3. |

Find the square root. -√36 | 36 is a perfect square when there is a non negative real number that multiplied by itself gives 36. 36 is a perfect square: 6*6=36. "-" means opposite so the answer is -6. |

Simplify by factoring. √x<sup>12</sup> | √x<sup>6*2</sup>. 2 goes with 2 from the radical and the answer is x<sup>6</sup> |

Approximate the square root to three decimal places. √10 | Since the radicand, 10, cannot be written as a perfect square, √10 is an irrational number. Use the calculator to approximate. 10^1/2 is approximately equal with 3.162. |

Find the root. <sup>3</sup>√8 | Write 8 as a perfect cube: 2*2*2=2<sup>3</sup>. Which means that the root of <sup>3</sup>√8 is 2. |

Simplify. <sup>3</sup>√(x<sup>12</sup>) | Simplify the radical: <sup>3</sup>√x. Summarize: x<sup>12/3</sup>=x^4 |

Simplify. √(-2<sup>2</sup>) | (a^n)^1/n. If n is an even positive integer, we have |a|. If n is an odd integer, we have a. Here we have |a|. The value of a is -2. |-2|=2. |

Simplify the radical. <sup>3</sup>√(-8x<sup>6</sup>*y<sup>12</sup>) | (a^n)^1/n. If n is an even positive integer, we have |a|. If n is an odd integer, we have a. Here we have |a|. Find the number which raised at 3rd power is -8. Simplify: <sup>3</sup>√(-8x<sup>6</sup>*y<sup>12</sup>)=-2x<sup>2</sup>*y<sup>4</sup> |

If g(x)=<sup>3</sup>√(x-10), find g(37). | Replace x in the function with 37. g(37)=<sup>3</sup>√(37-10). Simplify: g(37)=<sup>3</sup>√27. Simplify,if possible. g(37)=3. |

Find the square root. √81 | The positive square root of 81 is 9 because 9*9=81. |

Find the square root. -√400 | 400 is a perfect square when there is a non negative real number that multiplied by itself gives 400. 400 is a perfect square: 20*20=400. "-" means opposite so the answer is -20. |

Approximate the square root to three decimal places. √387 | Since the radicand, 387, cannot be written as a perfect square, √387 is an irrational number. Use the calculator to approximate. 387^1/2 is approximately equal with 19.672. |

Created by:
Giulian