Understanding Square Root Equations

The video tutorial addresses a common error in solving square root equations, specifically when the principal square root is set equal to a negative number, which is impossible. It explains the process of solving such equations by squaring both sides and highlights the importance of verifying solutions through substitution. The tutorial emphasizes that certain equations may appear solvable but actually have no solution, underscoring the need for careful verification.

Why can't the square root of a quantity be negative?

• Because square roots are always positive or zero.

• Because it is a rule in algebra.

• Because negative numbers do not exist.

• Because it is not possible to calculate.

What is the result of squaring both sides of the equation \( \sqrt{x + 2} = -3 \)?

• x + 2 = 0

• x + 2 = 3

• x + 2 = -9

• x + 2 = 9

What should you do after finding a solution to a square root equation?

• Assume it is correct.

• Verify by substituting back into the original equation.

• Ask a friend.

• Check with a calculator.

What does substituting the solution back into the original equation help determine?

• If the solution is easy.

• If the equation is difficult.

• If the solution is correct.

• If the equation is solvable.

What is a key takeaway when solving square root equations?

• Guess the answer.

• Always verify solutions.

• Never solve them.

• Use a calculator.