Simplifying Radicals with Variables

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 @@ ext{ } oot{2}{8}@@.

Back

@@ ext{ } oot{2}{8} = 2 ext{ } oot{2}{2}@@.

Front

What is the product property of square roots?

Back

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

Front

Simplify @@ ext{ } oot{2}{50}@@.

Back

@@ ext{ } oot{2}{50} = 5 ext{ } oot{2}{2}@@.

Front

What is the quotient property of square roots?

Back

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

Front

Simplify @@ ext{ } oot{2}{rac{16}{9}}@@.

Back

@@ ext{ } oot{2}{rac{16}{9}} = rac{4}{3}@@.

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 or higher powers from under the radical.

Front

Simplify @@ ext{ } oot{2}{x^4}@@.

Back

@@ ext{ } oot{2}{x^4} = x^2 ext{ } oot{2}{x^2}@@.

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.