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Cubed Roots, Add/sub Sq. Roots and non-square integers notes Absent notes Tues/Wed 5/6,7

Cubed Roots, Add/sub Sq. Roots and non-square integers notes Absent notes Tues/Wed 5/6,7. Example 1. Find the principal cubed root. 3 · 3 · 3 factor factor factor Solution. What is the radicand ? 27 is the radicand.

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Cubed Roots, Add/sub Sq. Roots and non-square integers notes Absent notes Tues/Wed 5/6,7

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  1. Cubed Roots, Add/sub Sq. Roots and non-square integers notes Absent notesTues/Wed 5/6,7

  2. Example 1 • Find the principal cubed root. 3 · 3 · 3 factor factor factor Solution • What is the radicand? • 27 is the radicand. • What is the index? And what does the index tell us? 3 • We need 3 of the same factor that when they are multiplied the answer is = to the radicand 27. • What is the principal root? • The principal root is the positive root. • What 3 factors (the same) can we multiply to equal the radicand? • 3 · 3 · 3 3

  3. Example 2 • Solve using principal root. 2 + 3 8 · 8 + 11 · 11 factor factor factor factor 2(8)+3(11) 16 + 33 49 Solution • What is another name of the radical sign? • It is a grouping. • What are the radicands? • 64 and 121 • What 2 factors (the same) can we multiply to each sq. root to equal the radicands? • We can multiply 8 and 8 • We can multiply 11 and 11. • What do we do with the 2 and 3 that are outside the radical signs? • We multiply them to the answers we get from the sq. rt’s because √ is a grouping. • What is the last step in order to get a solution? • We add the 2 answers. 49

  4. Example 3 • Solve using principal root. 2 - -7 2(7) - 7 14 - 7 = 7 Solution • What is another name of the radical sign? • Grouping • What is the radicand? • 49 • What 2 factors (the same) can we multiply to the sq. root to equal the radicand? • 7 x 7 • What do we do with the 2 onoutside the radical signs? • We multiply it to the sq. rt. Of 49. • What is the absolute value of -7? 7 • What is the last step in order to get a solution? • Subtract 14 and 7 7

  5. Example 4 • List to consecutive integers between which the number lies. (principal root) smaller perfect square Larger perfect square 4 · 4 5 · 5 factor factorfactorfactor • Solution • What does consecutive integers mean? • It mean one # followed by the next # ex: 2,3,4,5 • Is the sq. root of 17 a perfect square? YES or NO • What is the closest perfect square that is smaller than the sq. root of 17? • The closest perfect square is the sq. rt. of 16. • What is the closest perfect square that is larger than the sq. root of 17? • The closest perfect square is the sq. rt. of 25. • What are the principal roots to the perfect squares we found? • 4 and 5 4 and 5

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