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}@@.

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Back

To simplify radical expressions, look for perfect squares (or cubes) within the radicand and factor them out. For example, @@ ext{simplifying } oot{2}{8} = oot{2}{4 imes 2} = oot{2}{4} imes oot{2}{2} = 2 oot{2}@@.

Front

What is the product property of square roots?

Back

Front

What is the sum property of square roots?

Back

Front

Simplify: @@2 oot{7} + 3 oot{3} - 5 oot{7}@@

Back

@@-3 oot{7} + 3 oot{3}@@.

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Simplify: @@ oot{128}@@

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@@8 oot{2}@@.

Front

Simplify completely: @@-2 oot{15} imes oot{3}@@

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@@-6 oot{5}@@.

Front

Simplify completely: @@5 oot{15} imes 5 oot{5}@@

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@@125 oot{3}@@.

Front

Simplify completely: @@ oot{10} imes oot{5}@@

Back

@@5 oot{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, and 25 are perfect squares.