Simplifying Radical Expressions

Front

Define 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

What is the square root of a number?

Back

Front

Simplify the radical expression: @@ ext{ } oot{2}{72}@@

Back

@@6 oot{2}{2}@@.

Front

What is the product property of square roots?

Back

The product property states that @@ oot{2}{a} imes oot{2}{b} = oot{2}{a imes b}@@.

Front

Simplify the radical expression: @@ ext{ } oot{2}{200m^2n^4}@@

Back

@@10mn^2 oot{2}{2}@@.

Front

What is the quotient property of square roots?

Back

The quotient property states that @@ oot{2}{rac{a}{b}} = rac{ oot{2}{a}}{ oot{2}{b}}@@.

Front

Simplify the radical expression: @@ ext{ } oot{2}{32x^2y^3}@@

Back

@@4xy oot{2}{2y}@@.

Front

What does it mean to simplify a radical expression?

Back

To simplify a radical expression means to express it in its simplest form, removing any perfect squares from under the radical sign.

Front

Simplify the radical expression: @@ ext{ } oot{2}{50a^2b^3}@@

Back

@@5ab oot{2}{2b}@@.

Front

What is a perfect square?

Back

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