1 / 14

Solve Equations Using Nth Roots

Learn how to solve equations using nth roots. Practice examples involving nth roots, simplifying expressions, and using calculators. Apply this knowledge to estimate the length of coral cod based on its weight.

mkhan
Download Presentation

Solve Equations Using Nth Roots

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. a. 4x5 = 128 x5 = 32 x = 32  5 x 2 = EXAMPLE 4 Solve equations using nth roots Solve the equation. Divide each side by 4. Take fifth root of each side. Simplify.

  2. b. (x – 3)4 = 21 + x – 3 = 21 – 4  + x = 21 + 3 – 4  or 21 + 3 x = x = – 21 + 3 4  4  5.14 0.86 x or x EXAMPLE 4 Solve equations using nth roots Take fourth roots of each side. Add 3 to each side. Write solutions separately. Use a calculator.

  3. Biology A study determined that the weight w(in grams) of coral cod near Palawan Island, Philippines, can be approximated using the model w = 0.0167ℓ3 where l is the coral cod’s length (in centimeters). Estimate the length of a coral cod that weighs 200grams. EXAMPLE 5 Use nth roots in problem solving

  4. 0.0167 l 3 w = 0.0167 l 3 200 = 11,976 l 3 11,976 l  3 22.9 l A coral cod that weighs 200grams is about 23centimeters long. ANSWER EXAMPLE 5 Use nth roots in problem solving SOLUTION Write model for weight. Substitute 200 for w. Divide each side by 0.0167. Take cube root of each side. Use a calculator.

  5. x3 = 64 = 3 64 x x = 4 for Examples 4 and 5 GUIDED PRACTICE Solve the equation. Round the result to two decimal places when appropriate. 13.x3 = 64 SOLUTION take 3rd root of each side. Simplify.

  6. 14. x5 = 512 1 1 x5 = 512 2 2 x5 = 1024 x = 5 1024 x = 4 for Examples 4 and 5 GUIDED PRACTICE SOLUTION Multiply each side by 2. take5throot of each side. Simplify.

  7. 15. 3x2 = 108 3x2 = 108 x2 = 36 x = + 6 x = 2 36 – for Examples 4 and 5 GUIDED PRACTICE SOLUTION Divide each side by3. take2ndroot of each side. Simplify.

  8. 16. x3 x3 = 2 = 2 x3 = 8 x = 3 8 x = 2 1 1 4 4 for Examples 4 and 5 GUIDED PRACTICE SOLUTION Multiply each side by4. take 3rd root of each side. Simplify.

  9. 17. ( x – 2 )3 = –14 ( x – 2 )3 = –14 ( x – 2 ) = 3 –14 x = 3 –14 + 2 x = 3 –14 + 2 x = – 0.41 for Examples 4 and 5 GUIDED PRACTICE SOLUTION take 3rd root of each side. add 2 to both sides. Write solution. Use a calculator.

  10. 18. ( x + 5 )4 = 16 ( x + 5 )4 = 16 ( x + 5 ) = +4 16 x = + 4 16 – 5 or x = 2 – 5 x = – 2 – 5 x or x = – 3 = –7 for Examples 4 and 5 GUIDED PRACTICE SOLUTION take 4th root of each side. add 5 to each side. Write solutions separately. Use a calculator.

  11. WHAT IF? Use the information from Example 5 to estimate the length of a coral cod that has the given weight. 19. w = 0.0167l 3 275 = 0.0167l 3 16467 = l 3 3 16467 = l 25 = l for Examples 4 and 5 GUIDED PRACTICE a. 275grams SOLUTION Write model for weight. Substitute 275 for w. Divide each side by 0.0167. Take cube root of each side. Use a calculator.

  12. ANSWER A coral cod that has the 275grams is about 25 cm long. for Examples 4 and 5 GUIDED PRACTICE

  13. w = 0.0167l 3 = 0.0167l 3 340 20360 = l 3 3 20360 = l = l 27 A coral cod that has the 340grams is about 27 cm long. ANSWER for Examples 4 and 5 GUIDED PRACTICE b. 340grams SOLUTION Write model for weight. Substitute 340 for w. Divide each side by 0.0167 Take cube root of each side Use a calculator

  14. w = 0.0167l 3 450 = 0.0167l 3 26946 = l 3 = l 30 = l 3 26946 A coral cod that has the 450grams is about 30 cm long. ANSWER for Examples 4 and 5 GUIDED PRACTICE c. 450grams SOLUTION Write model for weight. Substitute 450 for w. Divide each side by 0.0167 Take cube root of each side Use a calculator

More Related