Solving Equations with Radicals

The video tutorial explains how to solve an equation with radicals on both sides. It begins by introducing the equation and the problem of radicals. The tutorial then demonstrates how to eliminate the radicals by squaring both sides of the equation. After removing the radicals, the focus shifts to isolating the variable x by transposing terms. Finally, the tutorial shows how to solve for x by simplifying and dividing, resulting in the solution x = 3.

What is the main issue with the equation 5x + 2 = 3x + 8?

• It is a quadratic equation.

• It has no solution.

• It has radicals on both sides.

• It has fractions.

What is the first step to solve the equation with radicals?

• Subtract both sides.

• Square both sides.

• Add both sides.

• Divide both sides.

After squaring both sides, what does the equation become?

• 5x + 2 = 3x + 8

• 5x - 2 = 3x - 8

• 5x + 2 = 3x - 8

• 5x - 2 = 3x + 8

Why do we square both sides of the equation?

• To eliminate fractions.

• To eliminate radicals.

• To make it a quadratic equation.

• To simplify the constants.

What happens to the radical sign after squaring?

• It becomes a constant.

• It is eliminated.

• It remains the same.

• It becomes a fraction.

What is the next step after removing the radicals?

• Add 3x to both sides.

• Subtract 3x from both sides.

• Divide both sides by 2.

• Multiply both sides by 2.

What operation is performed to isolate the variable x?

• Subtract 2 from both sides.

• Multiply both sides by 3.

• Add 2 to both sides.

• Divide both sides by 3.

What does transposing a term mean?

• Moving it to the other side with a sign change.

• Multiplying it by a constant.

• Subtracting it from both sides.

• Adding it to both sides.

What is the coefficient of x after transposing terms?

• 1

• 2

• 3

• 4

What is the simplified form of the equation after transposing terms?

• 2x = 6

• 3x = 8

• 2x = 8

• 3x = 6