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Square Root vocab. And Square Root Notes absent copy Tues/Wed 2/21,22

Square Root vocab. And Square Root Notes absent copy Tues/Wed 2/21,22.

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Square Root vocab. And Square Root Notes absent copy Tues/Wed 2/21,22

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  1. Square Root vocab. And Square Root Notesabsent copyTues/Wed 2/21,22

  2. Index Radical = Grouping Symbol Radicand = Term inside A Root is one of the factors of the radicand.What are two of the same roots (factors) that equals 9 (radicand) when you multiply? 3· 3=9 Or -3 · -3=9factor factorfactor factorYou can write the root as ± 3Principal root is always the Positive root (factor) What is the principal root of 9?3Indextells you how many of the same factors equals the radicand.Ex: 1 How many factors do we need to multiply to get the radicand?4 · 4 or -4 · -4 ± 4Ex: 2 How many factors do we need to multiply to get the radicand?2 · 2 · 2 · 2 ±2

  3. Variables always have a positive root because you don’t know if the variable represents a pos. or neg. #. Ex: 2 = h · h so the answer is hExponent rule: When bases are the same and you are multiplying you add the exponents. Ex: b2 · b2 = b2 +2 = b4When exponents are inside the radical sign find the same 2 factors of the exponent so when you add themthey equal the exponent. Ex: 8 = d4· d4 = d4+4 = d8factorfactor

  4. Example 1 • Find the two square roots. 15 · 15 factor factor -15 · -15 factor factor • What is the radicand? • A radicand is the term inside of the radical sign. 225 • What 2 factors (the same) can we multiply to equal the radicand?(Hint there are 2 sets of factors) • The 2 same factors are 15 and 15 or -15 and -15. • What is the best way to write down the solution? • The best way to write down the solution is to write it like: ± 15 15

  5. Example 2 • What is the principal root of this expression? 14 exponent rule = d7 • d7 = d7 +7= d14 11d7 · 11d7 factor factor Solution Solution • What is the radicand? • The radicand is 121d14 • What is the index and what does it mean? 2 • The index tell us how many factors = the radicand. 2 factors • What is the exponent rule we can use to factor the 14? • When bases are the same and we are multiplying we can add the exponents. • What 2 factors (the same) can we multiply to equal the radicand? • 11d7 · 11d7 • What does principal root mean? • Principal root is always the positive factor. 11d7

  6. Example 3 • If the flag of Switzerland has an area of 81 ft2, what is the length of each of its sides? The flag is square. (hint s = ) 9 • 9 9 ft factor factor9 ft Solution • What is the radicand? • The radicand is the area of the flag which is 81. • Do we only find the principal root? YES or NO • You can only have positive lengths. • What 2 factors (the same) can we multiply to equal the radicand? • The 2 factor that make up 81 are 9 and 9. • What is the length of each side? • The length of each side is 9 ft. flag Side = 9 ft

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