Solving Equations with Square Roots

The video tutorial explains how to solve an equation involving a principal square root. The strategy involves isolating the radical, squaring both sides to eliminate the radical, and solving the resulting linear equation. The importance of verifying the solution with the original equation is emphasized to ensure it aligns with the principal square root.

What is the first step in solving an equation with a square root?

• Divide both sides by a constant

• Multiply both sides by a constant

• Isolate the radical sign

• Add a constant to both sides

Why is it important to consider the principal square root when solving equations?

• To simplify the equation

• To ensure the solution is negative

• To avoid losing information about the square root

• To make the equation more complex

What operation is performed to isolate the radical sign in the equation 3 + √(5x + 6) = 12?

• Add 3 to both sides

• Divide both sides by 3

• Subtract 3 from both sides

• Multiply both sides by 3

What happens when you square both sides of the equation √(5x + 6) = 9?

• The equation becomes 5x + 6 = 9

• The equation becomes 5x + 6 = 45

• The equation becomes 5x + 6 = 81

• The equation becomes 5x + 6 = 18

After squaring both sides and simplifying, what is the next step to solve for x?

• Subtract 6 from both sides

• Divide both sides by 5

• Multiply both sides by 5

• Add 6 to both sides

What is the value of x after solving the equation 5x = 75?

• x = 10

• x = 15

• x = 12

• x = 18

Why is it necessary to verify the solution in the original equation?

• To ensure the solution is correct for the principal square root

• To verify the solution is an integer

• To check if the solution is negative

• To confirm the solution is a fraction

What is the result of substituting x = 15 back into the original equation?

• 3 + √81 = 12

• 3 + √90 = 12

• 3 + √60 = 12

• 3 + √75 = 12

What is the principal square root of 81?

• 9

• 10

• 7

• 8

What confirms that the solution x = 15 is correct?

• The equation becomes 3 + 8 = 12

• The equation becomes 3 + 11 = 12

• The equation becomes 3 + 9 = 12

• The equation becomes 3 + 10 = 12