A.EO.4: Simplifying Radical expressions

Front

What is a radical expression?

Back

A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, @@ ext{radical expression} = ext{ } oot{n}{x}@@.

Front

How do you simplify a square root?

Back

To simplify a square root, factor the number under the root into its prime factors, and then take out pairs of factors. For example, @@ ext{Simplify } ext{ } oot{2}{8} = oot{2}{4 imes 2} = 2 oot{2}@@.

Front

What is the square root of a product?

Back

The square root of a product can be expressed as the product of the square roots: @@ oot{2}{ab} = oot{2}{a} imes oot{2}{b}@@.

Front

What is the square root of a quotient?

Back

The square root of a quotient can be expressed as the quotient of the square roots: @@ oot{2}{rac{a}{b}} = rac{ oot{2}{a}}{ oot{2}{b}}@@.

Front

How do you simplify @@2 oot{56a^2b^2}@@?

Back

@@2 oot{56a^2b^2} = 4ab oot{14}@@.

Front

What is the simplified form of @@2 oot{18a^6b^2}@@?

Back

@@2 oot{18a^6b^2} = 6a^3b oot{2}@@.

Front

What is the process to simplify @@ oot{92a^2b^3}@@?

Back

Factor 92 as 4*23, then take out the square root of 4: @@ oot{92a^2b^3} = 2ab oot{23b}@@.

Front

What does it mean to simplify completely?

Back

To simplify completely means to reduce an expression to its simplest form, where no further simplification is possible.

Front

What is the importance of identifying perfect squares in simplification?

Back

Identifying perfect squares helps in simplifying radical expressions by allowing you to take square roots of those perfect squares out of the radical.

Front

What is a perfect square?

Back

A perfect square is a number that can be expressed as the square of an integer, such as 1, 4, 9, 16, etc.