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
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
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 on outside 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
Example 4 List to consecutive integers between which the number lies. (principal root) smaller perfect square Larger perfect square 4 · 4 5 · 5 factor factor factor factor 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
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