6.4-1 Check for Understanding

​Solving Radical Equations.

​When Solving Radical Equations, follow these steps.

​

​1. Get the radical by itself on one side of the equation.

​

​2. Raise both sides of the equation to the power of the index.

​

​3. Solve.

​

​* Always check your answers.

Multiple Choice

$$\sqrt{x+1}=4$$  
Step One is to Isolate the square root. Is the radical isolated?

• Yes. The Square Root is already isolated.

• No. Subtract 1 from both sides.

• No. Square both sides.

• No. Take the square root of 4.

Multiple Choice

Step Two is to Square Both Sides which looks like this:

$$\left(\sqrt{x+1}\right)^2=\left(4\right)^2$$  
Which of the following would result from this step?

• $$\sqrt{x+1}=16$$  
  

• $$\sqrt{x^2+1}=16$$  
  

• $$x+1=8$$  
  

• $$x+1=16$$  
  

Multiple Choice

So far, we have:

$$\sqrt{x+1}=4$$  
$$\left(\sqrt{x+1}\right)^2=\left(4\right)^2$$
$$x+1=16$$   
What should we do next?

• Nothing. x=16 is the solution.

• Add 1 to both sides.

• Subtract 1 from both sides.

• Subtract 16 from both sides.

Multiple Choice

$$\sqrt{x+1}=4$$  
Which of the following values would make this a true statement when substituted in for x?

• 3

• 8

• 15

• 16

Completed Problem

Multiple Choice

How about this one?

$$\sqrt{5x+1}=6$$  
Which of the following values would make this a true statement when substituted in for x?

• 36

• 7

• 6

• 1

Multiple Choice

Solve

• -14
• 14
• no solution
• 28

Poll

How are we feeling today?

Multiple Choice

Solve the equation: $$\sqrt[]{x+25}=\ 2$$  

• 5

• -5

• 23

• -21

Multiple Choice

Solve

• 102
• 12
• 98
• 7

Multiple Choice

$$\sqrt[]{4x\ +9}+6=\ 3$$

• No Solution

• 0

• -3

• 4.5