Question 1

Which of the following best describes a radical equation?

Accepted Answer

An equation where the variable appears inside a radical such as a square root or cube root.

Question 2

What is the first step when solving the equation $$\sqrt{x-1} = 3$$?

Accepted Answer

Isolate the radical.

Question 3

Solve the equation $$\sqrt{x-1} = 3$$ and select the correct solution.

Accepted Answer

$$x = 10$$

Question 4

Why is it important to check your solutions when solving radical equations?

Accepted Answer

Because squaring both sides can introduce extraneous solutions.

Question 5

Solve $$y - \sqrt{2y + 6} = 3. $$What is the first step?

Accepted Answer

Isolate the radical $$\sqrt{2y + 6}.$$

Question 6

After isolating the radical in $$y - \sqrt{2y + 6} = 3$$, what is the next step?

Accepted Answer

Raise both sides to the second power.

Question 7

Solve $$y - \sqrt{2y + 6} = 3. $$What is the solution?

Accepted Answer

$$y = 6$$

Question 8

Which of the following equations is quadratic in form?

Accepted Answer

$$(x^2$$ - $$3)^2$$ + $$5(x^2 - 3) - 6 = 0$

Question 9

Solve $$(x^2$$ - $$3)^2$$ + $$5(x^2 - 3) - 6 = 0$ for x$.

Accepted Answer

$$x = \pm 2$$

Question 10

Which method is most appropriate for solving $$x^4$$ + $$4x^2 - 5x = 36$?

Accepted Answer

Factoring

Question 11

What is the solution to $$x^4$$ + $$4x^2 - 5x - 36 = 0$?

Accepted Answer

$$x = 1 or$$ $$x = -3$$

Question 12

Which of the following is a possible extraneous solution for $$\sqrt{x+2} = x - 2$$?

Accepted Answer

$$x = 4$$

Question 13

If $$x + \sqrt{x} - 4 = 0$$, what substitution can you use to write it as a quadratic equation?

Accepted Answer

Let $$u = \sqrt{x}$$

Question 14

Which of the following best explains why squaring both sides of an equation can introduce extraneous solutions?

Accepted Answer

Because squaring is not a one-to-one function.

Question 15

Solve $$x + \sqrt{x} - 4 = 0$$ for $$x.$$

Accepted Answer

$$x = 4 or$$ $$x = 1$$

Radical Equations and Equations Quadratic in Form: Methods and Examples

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