1 / 20

Radicals

NCP 503: Work with numerical factors NCP 505: Work with squares and square roots of numbers NCP 507: Work with cubes and cube roots of numbers. Radicals. What is a radical?. Square roots, cube roots, fourth roots, etc are all radicals. They are the opposite of exponents.

albin
Télécharger la présentation

Radicals

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. NCP 503: Work with numerical factors NCP 505: Work with squares and square roots of numbers NCP 507: Work with cubes and cube roots of numbers Radicals

  2. What is a radical? • Square roots, cube roots, fourth roots, etc are all radicals. • They are the opposite of exponents. • √4 is asking what number times itself is equal to 4. (Answer is 2) • 3√8 is asking what number times itself “3” times is equal to 8. (Yup…the answer is 2 again.)

  3. Square & Cube Roots Cube Root Square Root √16 3√125 5 ∙ 5 ∙ 5 = 125 So, 3√125 = 5 4 ∙ 4 = 16 So, √16 = 4 Now you know what square and cube roots are, you can figure out the others…fourth root, fifth root, etc.

  4. How to find a cube root! Look for the x√ , to enter 3√125 Enter 3, x√, 125, and EXE.

  5. Try these… • 10 • 8 • 4 • 3 • 3√1000 = • 3√512 = • 3√64 = • 4√81 =

  6. Perfect Squares 2 ∙ 2 = 4, so 4 is a perfect square. Other perfect squares… 9 81 225 16 100 256 25 121 289 36 144 324 49 169 361 64 196 400 The square root of a perfect square is whole number. • √144 = 12

  7. Not So Perfect Squares Finding the square roots of other numbers results in a decimal. WE DO NOT WANT DECIMALS. NO DECIMALS! These will all end up as decimals. Remember: NO DECIMALS! • √50 • √32 • √20

  8. Simplifying Square Roots • √8 = • √4 ∙ √2 = • 2√2 8 is not a perfect square, so we will simplify it! √4 = 2 We can’t simplify √2, so we leave him alone. 8 is made up of 4 ∙ 2. Look! 4 is a perfect square! • √50 = • √25 ∙ √2 = • 5√2

  9. Try these… • = √9 ∙ √3 • = √16 ∙ √2 • = √4 ∙ √5 • = √25 ∙ √3 • = 3√3 • = 4√2 • = 2√5 • = 5√3 √27 √32 √20 √75

  10. Combining Square Roots To combine square roots, combine the coefficients of like square roots. • 4√3 + 5 √3 • = 9√3 They both have √3 in common, so we can add their coefficients. They both have √3 in common, so we can add their coefficients. • 7√2 – 4√2 = • 3√2 Works with subtraction also.

  11. Try these… • 3√5 + 5√5 • 5√7 – 8√7 • -2√3 + 7√3 • 7√11 – 4√11 • √6 + 2√6 • = 8√5 • = -3√7 • = 5√3 • = 3√11 • = 3√6

  12. Combining Square Roots We can combine multiple square roots! • 6√3 + 4√5 – 2√3 + 2√5 • = 4√3 • + 6√5 Combine the √3. Combine the √3. Next, combine the √5. Next, combine the √5. • 4√7 – 5√2 + 3√2 – 2√7 = • 2√7 – 2√2

  13. Try these… • = 3√5 + 3√7 • = 5√2 – 6√3 • = -7√6 + 3√5 • = -6√2 – 5√3 • -2√5 + 3√7 + 5√5 • 5√2 – 8√3 + 2√3 • -4√6 + 2√5 – 3√6 + √5 • √2 – 4√3 – 7√2 – √3

  14. Simplify and Combine √20 + √5 = √4 ∙ √5 + √5 = 3√5 2√5 + √5 = √12 + √27 = √3 ∙ √4 + √9 ∙ √3 = 3√3 = 2√3 + 5√3

  15. Multiplying Radicals When multiplying radicals, you can multiply the two numbers and put the answer under one radical. Simplify! √3 ∙ √2 = √6 √3 ∙ √3 = √9 = 3 √3 ∙ √6 = √18 = √9 ∙ √2 = 3√2

  16. Try This… = 7 √7 ∙ √7 = √49 √3 ∙ √5 = √15 √2 ∙ √6 = √12 = √4 ∙ √3 = 2√3 √15 ∙ √3 = √45 = √9 ∙ √5 = 3√5

  17. Multiplying Radicals • When multiplying radicals, you must multiply the coefficients AND the radicals. THE RADICALS DO NOT HAVE TO BE THE SAME! 2√5 ∙ 3√5 4√2 ∙ 2√8 Let’s see these two examples!

  18. Multiplying Radicals 2√5 ∙ 3√5 1. Multiply the coefficients. 2 ∙ 3 = 6 2. Multiply the radicals. √5 ∙ √5 = √25 3. Solve. 6√25 = 6 ∙ 5 = 30

  19. Multiplying Radicals 4√2 ∙ 2√3 1. Multiply the coefficients. 4 ∙ 2 = 8 2. Multiply the radicals. √2 ∙ √3 = √6 3. Simplify, if possible. 8√6

  20. Try This… 6√35 3√7 ∙ 2√5 = 2√3 ∙ 5√3 = 10√9 = 10 ∙ 3 = 30 4√2 ∙ 3√8 = = 12 ∙ 4 12√16 = 48 2√5 ∙ 3√2 = 6√10

More Related