Chapter 13 - Algebra Coach Exercises

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)