Simplifying Radical Expressions in Algebra 1

This video tutorial covers the simplification of radical expressions without using decimals, focusing on keeping expressions in radical form. It explains the properties of multiplication and division of square roots, and how to simplify radicals by removing perfect square factors. The tutorial also covers simplifying radicals with variables, combining radicals, and rationalizing the denominator. By the end of the lesson, students should be able to simplify various radical expressions and understand the importance of perfect square factors.

What is a key characteristic of radical expressions?

• They are always simplified using decimals.

• They always have an equal sign.

• They do not have an equal sign.

• They cannot be simplified.

Which property allows you to take the square root of factors separately?

• Multiplication property of square roots

• Division property of square roots

• Subtraction property of square roots

• Addition property of square roots

What is the simplified form of the square root of 50?

• 2√25

• 5√2

• 10√5

• 25√2

How do you simplify the square root of 27n^2?

• 3n√3

• 3√3n

• 27n

• 9√3n

What is the simplified form of the square root of 676?

• 26

• 27

• 25

• 24

What is the simplified form of 5√18c^2?

• 5√2c

• 3√2c

• 5c√2

• 15√2c

What is the simplified form of the square root of 144 divided by the square root of 9?

• 4

• 12

• 16

• 3

How do you rationalize the denominator of 1/√3?

• Multiply by √3/√3

• Multiply by √9/√9

• Multiply by 3/3

• Multiply by 1/√3

What is the simplified form of √5 / 3√2?

• √5 / 3

• √5 / 6

• √10 / 3

• √10 / 6

Which of the following is NOT a condition for a radical expression to be considered simplified?

• The radicand has no fractions.

• The radicand is a whole number.

• The radicand has no perfect square factors.

• The denominator has a radical in it.