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

Study Guide - Practice Questions