Add or subtract terms whenever possible. 7√5 + 13√5

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Identify the like terms in the expression. Here, both terms have the radical \( \sqrt{5} \), so they are like terms.

Rewrite the expression by factoring out the common radical \( \sqrt{5} \): \( 7\sqrt{5} + 13\sqrt{5} = (7 + 13)\sqrt{5} \).

Add the coefficients of the like terms inside the parentheses: \( 7 + 13 \).

Express the simplified form as the product of the sum of coefficients and the common radical: \( (7 + 13)\sqrt{5} \).

Leave the expression in this simplified form without calculating the final numeric value.

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주요 개념

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Like Terms in Algebra

Like terms are terms that have the same variable parts raised to the same powers. In the context of radicals, terms with the same radicand (number under the root) are considered like terms and can be combined by adding or subtracting their coefficients.

Simplifying Radicals

Simplifying radicals involves expressing the root in its simplest form by factoring out perfect squares or cubes. This process helps identify like terms and makes it easier to combine them when adding or subtracting.

Addition and Subtraction of Radical Expressions

When adding or subtracting radical expressions, only like radicals (same radicand and root) can be combined by adding or subtracting their coefficients. For example, 7√5 + 13√5 equals (7 + 13)√5 = 20√5.