Exploring Square Root Functions and Equations

This video tutorial covers square root functions, focusing on solving square root equations and inequalities. It explains extraneous solutions and provides step-by-step methods to solve these equations, including checking for extraneous roots. The tutorial includes multiple examples to illustrate the process and concludes with solving square root inequalities, emphasizing the importance of setting conditions for valid solutions.

What is an extraneous solution?

• A solution that is always positive

• A solution that does not satisfy the original equation

• A solution that satisfies the original equation

• A solution that is always negative

What is the first step in solving a square root equation?

• Get the square root by itself

• Subtract the constant term

• Check for extraneous roots

• Square both sides of the equation

In Example 1, what is the value of x after solving the equation?

• x = 4

• x = 2

• x = 0

• x = 1

In Example 2, why is there no solution to the equation?

• Because the equation has a negative square root

• Because the square root expression is not isolated

• Because the equation is quadratic

• Because the solution is extraneous

In Example 3, what are the two potential solutions for x?

• x = 7 and x = -6

• x = -7 and x = 6

• x = 6 and x = 7

• x = -6 and x = -7

In Example 4, what is the final solution for x?

• x = 4

• x = -4

• x = -2

• x = 2

What is the first step in solving a square root inequality?

• Check for extraneous roots

• Set the expression under the radical greater than or equal to zero

• Square both sides of the inequality

• Subtract the constant term

In the first inequality example, what is the range of x?

• x is between -2 and 25

• x is between 2 and -25

• x is between -2 and -25

• x is between 2 and 25

In the second inequality example, what is the solution for b?

• b is greater than 12

• b is greater than 43

• b is greater than 36

• b is greater than 7

In the third inequality example, why is there no solution?

• Because the inequality is quadratic

• Because the square root expression is not isolated

• Because the inequality produces an untrue statement

• Because the solution is extraneous