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Bell Work: In the expression 4ac, what is the constant?

Learn about exponents, square roots, and perfect squares, and how they are applied to simplify expressions and solve problems. Complete the homework assignment for practice.

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Bell Work: In the expression 4ac, what is the constant?

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  1. Bell Work: In the expression 4ac, what is the constant?

  2. Answer: 4

  3. Lesson 15:Powers and Roots

  4. Exponent*: Indicates how many times the base number is to be used as a factor. In the expression 5 , 5 is the base and 2 is the exponent. 2

  5. 3 In the expression 5 , we could also write it as 5 x 5 x 5 = 125. We read 5 as “five squared” and 5 as “five cubed.” We say “to the nth power” if the exponent n is greater than 3. For example, 5 is read as “five to the fourth power” or just “five to the fourth.” 2 3 4

  6. Example: Simplify 5 10 4 4

  7. Answer: 5 x 5 x 5 x 5 = 625 10 x 10 x 10 x 10 = 10,000 Notice that the number of zeros in 10,000 matches the exponent of 10.

  8. Example: Write the prime factorization of 72 using exponents.

  9. Answer: 72 = 2 x 2 x 2 x 3 x 3 72 = 2 x 3 3 2

  10. We can use exponents with units of length to indicate units of area. The formula for the area of a square is A = s . In this formula, A represents area and s represents the length of the side. 2

  11. Example: The figure shows a square floor tile that is one foot on each side. Find the are covered by the tile in square inches using the area formula. 12 inches

  12. Answer: A = 12 = 144 inches 2 2

  13. Exponents can be applied to variables. If the same variable is a factor in an expression a number of times, we can simplify the expression by writing the variable with an exponent.

  14. Example: Express with exponents. 2xxyyyz

  15. Answer: 2x y z 2 3

  16. Radical Expression*: an expression that indicates the root of a number. Radicand*: The number under a radical sign. Index*: Indicates a root of a number.

  17. The inverse of raising a number to a power is taking a root of a number. We may use a radical sign, √ , to indicate a root of a number. √25 = 5 √125 = 5 3

  18. If the index is 4 or more, we say “the nth root.” √9 = square root of 9 √27 = cubed root of 27 √125 = the fourth root of 125 3 4

  19. Example: Simplify √144 √27 3

  20. Answer: 12 x 12 = 144 = 12 3 x 3 x 3 = 27 = 3

  21. A number that is a square of a counting number is a perfect square. For example, 25 is a perfect square because 5 = 25. The number 64 is both a perfect square and a perfect cube. 2

  22. Is √64 less than or greater than √64? 3

  23. Answer: 8 x 8 = 64 and 4 x 4 x 4 = 64 √64 > √64 3

  24. Practice: The floor of a square room is covered with square foot tiles. If 100 tiles cover the floor, how long is each side of the room?

  25. Answer: √100 = 10 feet

  26. Practice: Name the first three counting numbers that are perfect squares. Then find their positive square roots.

  27. Answer: (1 x 1) = 1 (2 x 2) = 4 (3 x 3) = 9 √1 = 1 √4 = 2 √9 = 3

  28. HW: Lesson 15 #1-30 Due Next Time

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