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

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Identify the terms to be added: both are \( \sqrt{6} \). Since they are like terms (same radical part), you can combine them by adding their coefficients.

Rewrite each term with an explicit coefficient: \( 1 \times \sqrt{6} + 1 \times \sqrt{6} \).

Add the coefficients: \( 1 + 1 = 2 \).

Multiply the sum of the coefficients by the common radical: \( 2 \times \sqrt{6} \).

Write the final expression as \( 2\sqrt{6} \), which is the simplified form of the sum.

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Like Terms in Radicals

Radical expressions can be added or subtracted only if they have the same radicand (the number inside the root). For example, √6 and √6 are like terms because both have the radicand 6, allowing their coefficients to be combined.

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Rationalizing Denominators Using Conjugates

Simplifying Radicals

Before adding or subtracting radicals, it is important to simplify them if possible. Simplifying involves factoring the radicand to extract perfect squares, which can make combining terms easier or reveal like terms.

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Simplifying Trig Expressions

Combining Coefficients

When adding or subtracting like radicals, treat the radicals as variables and combine their coefficients. For example, √6 + √6 equals 2√6 because the coefficients 1 and 1 add up to 2.

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