Square Roots and Absolute Values

The video tutorial explains the mathematical principle that the square root of a squared number is equal to the absolute value of the number. It provides examples to illustrate this concept, including simplifying radical expressions with negative numbers. The tutorial also discusses applying this principle to variables, assuming they represent non-negative values, and concludes with further examples.

What is the result of squaring a number and then taking the square root?

• The original number

• The negative of the number

• The absolute value of the number

• Zero

Which of the following statements is true for any real number a?

• The square root of a squared is -a

• The square root of a squared is a

• The square root of a squared is the absolute value of a

• The square root of a squared is always zero

What is the principal square root of 9?

• 9

• 3

• -3

• 0

In the example with negative 3, what is the absolute value of negative 3?

• 3

• 0

• -3

• 9

What does the property of square roots and absolute values help us simplify?

• Only negative numbers

• Expressions with squared quantities under a radical

• Expressions without radicals

• Only positive numbers

If a variable is non-negative, how can we express the square root of its square?

• As the variable itself

• As the square of the variable

• As the negative of the variable

• As zero

What is the absolute value of 8a if a is non-negative?

• 8a

• -8a

• 0

• a

What is the principal square root of a squared term assuming non-negative variables?

• The term itself

• The negative of the term

• Zero

• The square of the term

How do we express the square root of a squared term if the variable is non-negative?

• As the square of the term

• As zero

• As the negative of the term

• As the absolute value of the term

What is the result of simplifying the square root of (a squared) if a is non-negative?

• a squared

• 0

• -a

• a