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

What does it mean to simplify a radical expression?

Back

To simplify a radical expression means to rewrite it in a simpler form, often by removing perfect squares or cubes from under the radical sign.

Front

What is the square root of a number?

Back

Front

How do you simplify @@ ext{ } oot{2}{x^2}@@?

Back

@@ ext{ } oot{2}{x^2} = x@@, since the square root of a square returns the base.

Front

What is the product property of square roots?

Back

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

Front

How do you simplify @@ ext{ } oot{2}{48}@@?

Back

@@ ext{ } oot{2}{48} = ext{ } oot{2}{16 imes 3} = ext{ } oot{2}{16} imes ext{ } oot{2}{3} = 4 ext{ } oot{2}{3}@@.

Front

What is the quotient property of square roots?

Back

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

Front

How do you simplify @@ ext{ } oot{2}{300}@@?

Back

@@ ext{ } oot{2}{300} = ext{ } oot{2}{100 imes 3} = ext{ } oot{2}{100} imes ext{ } oot{2}{3} = 10 ext{ } oot{2}{3}@@.

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, and 25 are perfect squares.

Front

How do you simplify @@ ext{ } oot{2}{25x^6}@@?

Back

@@ ext{ } oot{2}{25x^6} = ext{ } oot{2}{25} imes ext{ } oot{2}{x^6} = 5x^3@@.