Solving Equations with Roots

This video tutorial covers solving equations involving square roots, emphasizing the importance of inverse operations. It explains how to isolate variables and solve equations step-by-step, highlighting common mistakes and providing tips to avoid them. The tutorial includes advanced examples and practice problems to reinforce learning.

What is the primary difference between an expression and an equation?

• An expression always includes numbers, an equation does not.

• An equation has equal sides, an expression does not.

• An equation can be graphed, an expression cannot.

• An expression includes variables, an equation does not.

What is the inverse operation of addition?

• None of the above

• Multiplication

• Subtraction

• Division

What is the result of squaring the square root of 4?

• 16

• 2

• 4

• 8

What is the correct result when you square the square root of 16?

• 32

• 16

• 8

• 4

To solve the equation with a square root, what must you do first?

• Isolate the square root

• Add one to both sides

• Divide by the coefficient of the square root

• Square both sides immediately

If you have the equation 2√x = 6, what is the first step to solve it?

• Add 6 to both sides

• Subtract 2 from both sides

• Divide both sides by 2

• Square both sides

What do you achieve by squaring both sides of an equation involving a square root?

• You reduce the equation to its simplest form

• You double the values

• You eliminate the square root

• You isolate the variable

After isolating the square root in the equation √x + 2 = 4, what is the next step?

• Subtract 2 from both sides

• Add 2 to both sides

• Divide both sides by 2

• Square both sides

How do you handle an equation like √(x-5) = 7 to isolate x?

• Subtract 5 from both sides

• Add 5 to both sides after squaring

• Multiply both sides by 5

• Divide both sides by 5

In the equation 3√2 = √x, after dividing by 3, what is the correct way to solve for x?

• Subtract 2 from both sides

• Add 3 to both sides

• Square both sides

• Divide both sides by 2