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Algebra

Algebra. Square and Cube Roots. Warm-up. Expand . Calculate if n=7. Find the area of the following square:. 2,401. A = 81 cm 2. 9 cm. Warm-up cont’d. 4) What is the length of the side of this square that has an area of 25 cm 2. 25 cm 2. 5 cm. ?. Warm-up cont’d.

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Algebra

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  1. Algebra Square and Cube Roots

  2. Warm-up • Expand . • Calculate if n=7. • Find the area of the following square: 2,401 A = 81 cm2 9 cm

  3. Warm-up cont’d • 4) What is the length of the side of this square that has an area of 25 cm2. 25 cm2 5 cm ?

  4. Warm-up cont’d • 5) What is the length of the side of this square that has an area of 100 cm2. 100 cm2 10 cm ?

  5. Definition of square root • The square root of a number, written , is the number that when multiplied by itself is equal to the number under the square root sign. • Example: because

  6. Practice • Calculate each: =7 =8.3

  7. Both Roots • Square roots actually have two answers, a positive and negative answer. • 3) Find both roots of • 7 and -7 (because too.) • This is often written as

  8. Negative Roots • You cannot find the square root of a negative number because the same number multiplied by itself will never be negative. • 4) Evaluate • Can’t do it, no number times itself = -25.

  9. Negative of a Root • 5) Evaluate • First, do the square root, then use the negative root as your answer. • isn’t the same as

  10. Square root vs. square • The square root andsquare undo each other. • 6) Find • , and , so • 7) Find • 8) Find

  11. Square root vs. square • The square root andsquare undo each other. • 9) Find • , and , so • 10) Find • 11) Find

  12. Solving Square root equations • Since the square root undoes the square, we can use it to solve equations like by taking the square root of both sides of the equation. • 12) Solve • Take the square root (of both sides) to get back to .

  13. Cont’d • 13) Solve

  14. Cube roots • A cube root of a number is one of three equal factors of the number. • Example: 2 is the cube root of 8 because . • Cube root is written with the symbol • 14) Find =4 because

  15. Negative cube roots • It is possible to find the cube root of a negative number because the product of three negatives is negative. • 15) Find = -6

  16. Solving cube root equations • Solve cube equations like you would square equations, just take the cube root of both sides instead of the square root. • 16) Solve • (take cube root of both sides)

  17. Volume • 17) Find the volume of the cube. 8 cm

  18. Volume • 18) Find the length of the cube’s side. V = 27

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