Simplifying Radical Expressions: Key Techniques and Examples

Nancy explains how to simplify radicals and radical expressions, focusing on square roots. She covers simplifying perfect squares, non-perfect squares, products, and quotients, and introduces the concept of using conjugates for more complex expressions. The video provides step-by-step instructions and examples to help viewers understand the process of simplifying square root problems.

What is the main focus of the video?

• Simplifying fractions

• Graphing linear equations

• Simplifying radicals and radical expressions

• Solving quadratic equations

What is the square root of 81?

• 10

• 9

• 8

• 7

If the number under the square root is not a perfect square, what should you do?

• Multiply by 2

• Subtract 1

• Find a perfect square that divides evenly into the number

• Divide by 1

What is the simplified form of sqrt(125)?

• 5 x sqrt(5)

• 10 x sqrt(5)

• 25 x sqrt(5)

• 15 x sqrt(5)

How do you simplify a product involving a square root, such as 5 x sqrt(54)?

• Divide by 2

• Find a perfect square that divides evenly into 54

• Multiply by 3

• Subtract 5

What is the simplified form of 4 x sqrt(31)?

• 2 x sqrt(31)

• 16 x sqrt(31)

• 4 x sqrt(31)

• 8 x sqrt(31)

Why is it considered simpler to remove the square root from the denominator?

• It makes the expression harder to understand

• It is a standard mathematical convention

• It makes the expression more complex

• It makes the expression longer

What is the simplified form of 4 / sqrt(2)?

• 1 x sqrt(2)

• 2 x sqrt(2)

• 4 x sqrt(2)

• 8 x sqrt(2)

What is the conjugate of 5 - sqrt(3)?

• 5 + sqrt(3)

• 5 - sqrt(3)

• sqrt(3) + 5

• sqrt(3) - 5

What is the final simplified form of the expression 4 / (5 - sqrt(3))?

• 23 + 9 x sqrt(3) over 22

• 23 - 9 x sqrt(3) over 22

• 23 + 5 x sqrt(3) over 22

• 23 - 5 x sqrt(3) over 22