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

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Identify the like terms in the expression. Here, both terms contain the square root of 3, so they are like terms: \(5\sqrt{3}\) and \(\sqrt{3}\).

Rewrite the expression to clearly show the coefficients of the like terms: \(5\sqrt{3} - 1\sqrt{3}\).

Subtract the coefficients of the like terms while keeping the square root part unchanged: \((5 - 1)\sqrt{3}\).

Simplify the subtraction inside the parentheses: \(4\sqrt{3}\).

Write the final simplified expression as \(4\sqrt{3}\), which is the result of the subtraction.

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Like Terms in Radicals

Radical expressions can be combined only if they have the same radicand (the number inside the root). For example, terms with √3 can be added or subtracted by combining their coefficients, similar to combining like terms in algebra.

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Rationalizing Denominators Using Conjugates

Simplifying Radicals

Before adding or subtracting radicals, ensure each radical is in its simplest form. Simplifying involves factoring out perfect squares from under the root to make combining terms easier and more accurate.

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Simplifying Trig Expressions

Arithmetic with Coefficients

When adding or subtracting like radicals, treat the coefficients (numbers in front) as regular numbers. For example, 5√3 - √3 equals (5 - 1)√3 = 4√3, by subtracting the coefficients 5 and 1.

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