Solving Equations Involving Radicals

The video tutorial explains how to solve equations involving radicals. It starts with an equation where the radical is already isolated, demonstrating the process of squaring both sides to eliminate the square root and solve for the variable. The tutorial then addresses a more complex equation where the radical is not isolated, showing how to first isolate the radical before squaring both sides to solve for the variable. The key steps include isolating the radical, squaring both sides, and solving for the variable.

What is the first step in solving an equation with a radical that is already isolated?

• Multiply both sides by 2

• Subtract a constant from both sides

• Add a constant to both sides

• Square both sides of the equation

After squaring both sides of the equation, what is the next step to isolate the variable X?

• Multiply both sides by 3

• Add 1 to both sides

• Divide both sides by 3

• Subtract 1 from both sides

What happens to the square root when you square both sides of an equation?

• It becomes negative

• It cancels out

• It remains unchanged

• It doubles

In the first example, what is the value of X after solving the equation?

• X = 4

• X = 5

• X = 3

• X = 2

In the second example, what is the first step to isolate the radical?

• Multiply both sides by 10

• Subtract 10 from both sides

• Add 10 to both sides

• Divide both sides by 10

What is the result of squaring both sides of the equation in the second example?

• 10X + 1 = 9

• 10X - 1 = 9

• 10X - 1 = 3

• 10X + 1 = 3

What is the final value of X in the second example?

• X = 3

• X = 2

• X = 1

• X = 0

What is the general method to solve equations involving radicals?

• Isolate the radical and then add a constant

• Isolate the radical and then multiply by a constant

• Isolate the radical and then square both sides

• Isolate the radical and then divide by a constant

What is the purpose of isolating the radical in an equation?

• To eliminate the variable

• To make the equation more complex

• To prepare for squaring both sides

• To simplify the equation