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

What does it mean to simplify a radical expression?

Back

Simplifying a radical expression means to rewrite it in a simpler form, often by factoring out perfect squares or cubes from under the radical.

Front

What is the square root of a number?

Back

Front

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

Back

@@ ext{ } oot{2}{a^2} = a@@, since the square root of a squared term is the base itself.

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}{ab}@@.

Front

What is the quotient property of square roots?

Back

Front

How do you simplify @@ ext{ } oot{2}{18}@@?

Back

@@ ext{ } oot{2}{18} = ext{ } oot{2}{9 imes 2} = 3 ext{ } oot{2}{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.

Front

How do you simplify @@ ext{ } oot{2}{a^4}@@?

Back

@@ ext{ } oot{2}{a^4} = a^2@@, since the square root of a raised to an even power is half the exponent.

Front

What is the simplified form of @@ ext{ } oot{2}{32}@@?

Back

@@ ext{ } oot{2}{32} = ext{ } oot{2}{16 imes 2} = 4 ext{ } oot{2}{2}@@.