Radical Expressions: Simplify and Combine

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, factor the number under the radical into its prime factors and look for pairs of factors. For example, @@ ext{simplifying } ext{ } oot{2}{18} = oot{2}{9} imes oot{2}{2} = 3 oot{2}@@.

Front

What is the square root of 72?

Back

@@ ext{The square root of 72 is } 6 oot{3}@@.

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How do you combine like radicals?

Back

To combine like radicals, add or subtract the coefficients of the radicals that have the same index and radicand. For example, @@3 oot{5} + 2 oot{5} = 5 oot{5}@@.

Front

What is the simplified form of @@ oot{2}{18} + oot{2}{8}@@?

Back

@@ ext{The simplified form is } 5 oot{2}@@.

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What is the principle of simplifying square roots?

Back

The principle of simplifying square roots involves finding perfect squares within the radicand. For example, @@ oot{2}{50} = oot{2}{25} imes oot{2}{2} = 5 oot{2}@@.

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What does it mean to rationalize the denominator?

Back

Front

What is the sum of @@3 oot{2} + 4 oot{2}@@?

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@@ ext{The sum is } 7 oot{2}@@.

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How do you simplify @@ oot{2}{32}@@?

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@@ ext{The simplified form is } 4 oot{2}@@.

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@@ ext{The difference is } oot{2}{a} - oot{2}{b}@@, which cannot be simplified further unless a and b are known.