Understanding Square Roots and Absolute Values

The video tutorial explains how to simplify a given expression by rewriting it as a square root of a perfect square trinomial. It begins by expressing numbers in a different form and then factors the expression into a perfect square trinomial. The tutorial further explains the properties of square roots and the necessity of using absolute values to ensure positive results. The final expression is simplified to the absolute value of 1 minus the square root of two, which is rewritten as the square root of two minus one.

What is the first step in simplifying the given expression?

• Write it as a fraction

• Multiply by a constant

• Express it as a square root of a quantity

• Convert it to a decimal

How is the number 3 rewritten in the simplification process?

• As 1.5 + 1.5

• As 3 + 0

• As 1 + 2

• As 2 + 1

What is a perfect square trinomial?

• A trinomial that can be factored into a square of a binomial

• A trinomial with three different terms

• A trinomial that cannot be factored

• A trinomial with only positive terms

Which of the following is a factor of the square root of two?

• Square root of two

• 2

• Zero

• 1

Why is the absolute value used in the final expression?

• To ensure the result is positive

• To ensure the result is negative

• To convert it to a fraction

• To simplify the expression further

What is the final simplified form of the expression?

• Square root of two plus one

• Square root of two minus one

• One minus square root of two

• Two minus square root of one