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 any perfect squares or cubes from under the radical sign.

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}{8}@@?

Back

@@ ext{ } oot{2}{8} = oot{2}{4 imes 2} = oot{2}{4} imes oot{2}{2} = 2 oot{2}@@.

Front

What is the value of @@ ext{ } oot{3}{27}@@?

Back

@@ ext{ } oot{3}{27} = 3@@.

Front

What is the product property of square roots?

Back

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

Front

What is the sum of @@ ext{ } oot{4}{16} + 2@@?

Back

@@ ext{ } oot{4}{16} + 2 = 4 + 2 = 6@@.

Front

How do you simplify @@2( oot{9} imes oot{36}) - oot{196}@@?

Back

@@2( oot{9} imes oot{36}) - oot{196} = 2(3 imes 6) - 14 = 36 - 14 = 22@@.

Front

What is the value of @@4^2 + oot{25} - 12@@?

Back

@@4^2 + oot{25} - 12 = 16 + 5 - 12 = 9@@.

Front

Which of the following is NOT a perfect square: 1, 4, 100, 8?

Back

8 is NOT a perfect square.