University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

499

Pages:

3
Author:

efreet4ifh37v

Solving Radical Equations In your own words, write the meaning of each vocabulary term. radical equation = remember hints move outside -> inside when √ ... there are usually 2 answers +/- Core Concepts Squaring Each Side of an Equation Words: If two expressions are equal, then their squares are also equal. Algebra: If a = b, then 1 a² = b². 5:5 5² = 5² Extra Practice In Exercises 1-21, solve the equation. Check your solution(s). √x = 4 (√x)² = (4)² x = 16 check √16 = 4 4 = 4 √n - 3 = 8 +3 +3 (√n)² = (11)² n = 121 3√a - 15 = -6 +15 +15 (3√a)/3 = 9/3 (√a)² = (3)² a = 9 √x - 3 + 7 = 11 -7 -7 (√x - 3)² = (4)² x - 3 = 16 +3 +3 x = 19 (6√t - 2)/6 = 12 6√t - 2 = 72 +2 +2 (6√t)/6 = 74/6 (√t)² = (37/3)² t = 1369/9 3√x - 6 = 20 +6 +6 (3√x)/3 = 26/3 (√x)² = (26/3)² x = 676/9 7. (√d) = (√5d - 8)² d = 5d - 8 -4d = -8 d = 2 Check: √2 = √(5 * 2 - 8) √2 = √2 8. (√3c - 2) = (√4c - 6)² 3c - 2 = 4c - 6 -c = -4 c = 4 Check: √(3 * 4 - 2) = √(4 * 4 - 6) √10 = √10 9. (√4b - 4) = (√2b + 4)² 4b - 4 = 2b + 4 2b = 8 b = 4 Check: √(4 * 4 - 4) = √(2 * 4 + 4) √12 = √12 10. √(z - 12) = (√(2/3)z - 3)² z - 12 = (2/3)z - 3 -1/3z = 9 z = -27 Check: √(-27 - 12) = √(2/3 * -27 - 3) √-39 = √-18 (Not true, extraneous solution) 11. √(3w + 1) - √(6w) = 0 √(3w + 1) = √(6w) 3w + 1 = 6w 1 = 3w 1/3 = w Check: √(3 * 1/3 + 1) - √(6 * 1/3) = 0 √2 - √2 = 0 12. √(3v + 1) = √(6w) + 1 (√(3v + 1))² = (√(6w) + 1)² 3v + 1 = 6w + 2√(6w) + 1 3v = 6w + 2√(6w) (3v)² = (6w + 2√(6w))² 9v² = 36w² + 24w√(6w) + 4w 9v² - 36w² - 4w = 24w√(6w) (9v² - 36w² - 4w)² = (24w√(6w))² 81v⁴ - 648v²w² - 72v²w + 1296w⁴ + 32w² - 16vw = 576w³ 13. (√(x + 1)) = (√(x + 2))² x + 1 = x + 2 1 = 2 Extraneous Solutions 14. (√(3y + 2)) = (√(y + 2))² 3y + 2 = y + 2 2y = 0 y = 0 Check: √(3 * 0 + 2) = √(0 + 2) √2 = √2 15. (√(7m - 3)) = (√(m + 9))² 7m - 3 = m + 9 6m = 12 m = 2 Check: √(7 * 2 - 3) = √(2 + 9) √11 = √11 16. (k + 6)² = (√(2k + 15))² k² + 12k + 36 = 2k + 15 k² + 10k + 21 = 0 (k + 3)(k + 7) = 0 k = -3, k = -7 Extraneous 17. (√(-1 - 2b))² = b² -1 - 2b = b² b² + 2b + 1 = 0 (b + 1)(b + 1) = 0 b = -1 Extraneous 18. (√(3p + 19))² = (p - 1)² 3p + 19 = p² - 2p + 1 0 = p² - 5p - 18 0 = (p - 9)(p + 2) p = 9, p = -2 Extraneous 19. (r - 1)² = (√(r + 5))² r² - 2r + 1 = r + 5 r² - 3r - 4 = 0 (r - 4)(r + 1) = 0 r = 4, r = -1 Extraneous 20. (√(2x - 1))² = (6 - 3)² 2x - 1 = 9 2x = 10 x = 5 Extraneous 21. (k - 1)² = (√(5k - 9))² k² - 2k + 1 = 5k - 9 k² - 7k + 10 = 0 (k - 5)(k - 2) = 0 k = 5, k = 2