Simplifying Radical Expressions

The video tutorial explains how to simplify radical expressions without using a calculator. It covers three examples: simplifying √(21 - 8√5), √(16 - 6√7), and √(39 + 12√3). The tutorial demonstrates the use of perfect square trinomials to simplify these expressions and verifies the results by expanding the simplified forms. The video concludes with a summary and links to additional resources.

What is the first step in simplifying a radical expression like the square root of 21 minus 8 square root 5?

• Multiply the terms inside the square root.

• Directly subtract the terms inside the square root.

• Identify if the expression is a perfect square trinomial.

• Use a calculator to find the square root.

In the expression square root of 21 minus 8 square root 5, what does 'a' equal when b is the square root of 5?

• 3

• 5

• 2

• 4

How do you verify the solution to the expression square root of 21 minus 8 square root 5?

• By adding the terms inside the square root.

• By multiplying the expression by itself and checking the result.

• By subtracting the terms inside the square root.

• By using a calculator to check the square root.

What is the value of 'a' in the expression square root of 16 minus 6 square root 7?

• 3

• 4

• 2

• 5

What is the final simplified form of the expression square root of 16 minus 6 square root 7?

• 3 minus the square root of 7

• 3 plus the square root of 7

• 4 plus the square root of 7

• 4 minus the square root of 7

In the expression square root of 39 plus 12 times the square root of 3, what is the value of 'b'?

• Square root of 2

• Square root of 3

• Square root of 5

• Square root of 7

What is the final simplified form of the expression square root of 39 plus 12 times the square root of 3?

• 7 minus the square root of 3

• 7 plus the square root of 3

• 6 minus the square root of 3

• 6 plus the square root of 3

What is the purpose of checking if a radical expression fits a perfect square trinomial?

• To determine if a calculator is needed.

• To add the terms inside the square root.

• To simplify the expression more easily.

• To find the exact square root value.

What is a key indicator that a radical expression might be a perfect square trinomial?

• The expression has more than two terms.

• The expression can be rewritten as a squared term.

• The presence of a plus sign.

• The presence of a minus sign.

What should you do if you encounter a radical expression on a test?

• Skip the question.

• Guess the answer.

• Check if it fits a perfect square trinomial.

• Immediately use a calculator.