Solving Radical Equations and Fractions

The video tutorial explains how to solve a radical equation by isolating the radical, simplifying the equation, solving for x, and rounding the solution to four decimal places. It also includes verifying the solution by substituting it back into the original equation to ensure accuracy.

What is the first step in solving a radical equation with one radical?

• Add a constant to both sides

• Isolate the radical on one side

• Square both sides immediately

• Multiply both sides by a constant

After isolating the radical, what operation is performed next?

• Add a constant to both sides

• Multiply both sides by the radical

• Divide both sides by the coefficient of the radical

• Subtract a constant from both sides

What is the purpose of squaring both sides of the equation?

• To simplify the equation

• To find the common denominator

• To eliminate the radical

• To isolate the variable

What is the common denominator used to add fractions in this problem?

• 3

• 9

• 6

• 12

What is the square of four-thirds?

• 12/9

• 16/9

• 8/3

• 4/3

How do you express the solution as an improper fraction?

• By finding a common denominator

• By adding the fractions directly

• By subtracting the fractions

• By multiplying the fractions

What is the decimal approximation of the solution rounded to four decimal places?

• 3.7788

• 3.7777

• 3.7778

• 3.7780

Why is it important to verify the solution of a radical equation?

• To check if the solution is positive

• To confirm the solution satisfies the original equation

• To find an alternative solution

• To ensure the solution is a whole number

What is the result of substituting the solution back into the original equation?

• The equation is not satisfied

• The equation becomes undefined

• The equation results in a different solution

• The equation is satisfied

What is the final step in verifying the solution?

• Subtracting the solution from the original equation

• Dividing the solution by the original equation

• Multiplying the solution by the original equation

• Checking if both sides of the equation are equal