Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Survey

Document related concepts

Transcript

Symbols Defn: a is the positive (or principal) square root of a. It is the positive number whose square is a. Every radical expression contains three parts: index Radical symbol 3 64 radicand This expression represents the number we must cube to get 64. Because 43 64 , we say that 3 64 4 NOTE: When an index is not shown, it is assumed to be a 2. You might want to memorize the first few square and cube roots? 1 1 4 2 9 3 3 1 1 3 82 3 27 3 3 64 4 3 125 5 16 4 25 5 36 6 49 7 64 8 81 9 100 10 121 11 144 12 Radical Facts: The even power of a real number is always 4 positive or zero. (2) 2 2 2 2 16 Thus, an even root of a negative number is 4 16 undefined on the set of real numbers. An odd root of a 3 negative number will 8 2 always be negative. Keep It Straight! The negative square root of 9 is -3! 9 3 Where the square root of 9 a negative number is undefined on the set of real numbers. Now,You’ve Got It! Radicals with Fractions Keep your cool! It is easy. 4 4 2 25 25 5 Just take the square root of the numerator AND take the square root of the denominator! Examples: 16 4 121 11 4 81 3 3 27 3 0 0 Remember: it is okay to have a negative radicand if the root odd.. We just get a NEGATIVE ANSWER! Rational or Irrational, that is the question? Some radicals come out nice and easy.. Others not so nice.. Since there is no number that raised to the third power gives us 12, our calculator has to approximate it: 7 7 7 7 7 4 2401 3 12 2.289428485... 4 If the decimal approximation terminates or repeats it is a rational number. If the decimal approximation does not terminate or repeat, it is called an irrational number.