Add or subtract, as indicated. See Example 6. 2√3 + 5√3

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Identify the like terms in the expression. Here, both terms have the radical \( \sqrt{3} \), so they are like terms.

Write the expression by factoring out the common radical \( \sqrt{3} \): \( 2\sqrt{3} + 5\sqrt{3} = (2 + 5)\sqrt{3} \).

Add the coefficients of the like terms inside the parentheses: \( 2 + 5 = 7 \).

Rewrite the expression with the sum of the coefficients multiplied by the common radical: \( 7\sqrt{3} \).

This is the simplified form of the expression, combining the like radical terms.

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Like Terms in Algebra

Like terms are terms that have the same variable parts raised to the same powers. In this question, the terms involve the same radical expression (√3), so they can be combined by adding or subtracting their coefficients.

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Algebraic Operations on Vectors

Simplifying Radicals

A radical expression involves roots, such as square roots. Simplifying radicals means expressing them in their simplest form. Here, both terms have the same radical (√3), so no further simplification of the radical is needed before combining.

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Simplifying Trig Expressions

Addition and Subtraction of Radicals

You can only add or subtract radicals that have the same radicand (the number inside the root). This process is similar to combining like terms in algebra, where you add or subtract the coefficients while keeping the radical part unchanged.

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