Chapter 13 - Algebra Coach Exercises


Algebra Coach Exercise on radicals.
Simplify each of the following expressions involving radicals. To do this drag-and-drop each of them into the Algebra Coach and click the Simplify button. For number 10, first factor the radicand by clicking on Factor.
  1. 1 / sqrt(15)
  2. sqrt(3) * sqrt(7)
  3. sqrt(3) / sqrt(7)
  4. sqrt(3 / 7)
  5. sqrt(9 x^2 + 9 y^2 + 18 x y)

  6. sqrt(6) sqrt(10)
  7. sqrt(5 x^4)
  8. sqrt(9 a^2)
  9. sqrt(a^2 b^4 / c^6)
  10. sqrt(45 x^4 + 9 x^2)

Algebra Coach Exercise on radical equations.
Solve each of the following radical equations. To do this drag-and-drop each of them into the Algebra Coach and click the AutoSolve button.
  1. sqrt(x^2 - 6x) = x - 9
  2. sqrt(x - 32) + sqrt(x) = 16
  3. sqrt(x - 3) + 1/sqrt(x - 3) = sqrt(x)
  4. sqrt(x + 1) = sqrt(2x - 7)
  5. sqrt(x - 3) = 4/sqrt(x - 3)

  6. x + 2 = sqrt(x^2 + 6)
  7. sqrt(x^2 - 7.25) = 8.75 - x
  8. sqrt(x - 15.5) = 5.85 - sqrt(x)
  9. 6/sqrt(3 + x) = sqrt(x + 3)
  10. sqrt(12 + x) = 2 + sqrt(x)

  11. sqrt(x^2 - 2x - sqrt(1 - x)) = 1 - x
  12. sqrt(1/x) - sqrt(x) = sqrt(1 + x)
  13. sqrt(x - 2) - sqrt(x) = 1/sqrt(x - 2)
  14. sqrt(5x - 19) - sqrt(5x + 14) = - 3
  15. Z = sqrt(R^2 + (wL - 1/w/x)^2)