Understanding the Principle Square Root

The video addresses a common misconception that the principal square root of x squared equals x. It uses the example of x equals negative three to show that this is incorrect, as the principal square root of nine is positive three, not negative three. The correct equation is that the principal square root of x squared equals the absolute value of x. This ensures that the result is always non-negative, aligning with the definition of the principal square root.

Why is the statement 'the principle square root of x squared equals x' incorrect when x is negative?

• Because x squared is always positive.

• Because negative numbers do not have square roots.

• Because the principle square root is always positive.

• Because the square root of a negative number is undefined.

What is the principle square root of 9?

• Nine

• Positive three

• Zero

• Negative three

What is the correct equation for the principle square root of x squared?

• The principle square root of x squared equals the absolute value of x.

• The principle square root of x squared equals x.

• The principle square root of x squared equals zero.

• The principle square root of x squared equals negative x.

When x equals negative three, what does the principle square root of x squared equal?

• Zero

• Negative three

• Nine

• Positive three

What does the absolute value of a number represent?

• Zero

• The negative value of the number

• The positive value of the number

• The number itself