Algebra 1 Intermediate

Radical Operations

Add, subtract, multiply, or divide radical expressions — simplify radicals to like terms and combine step by step.

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Adding Like radicals: Yes
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Step-by-Step Solution
Adding & Subtracting Radicals
a√n ± b√n = (a ± b)√n

Only like radicals — same index and same radicand — can be combined. First simplify each radical completely, then check if the radicands match.

If the radicands are different even after simplification, the expression is already in simplest form and cannot be combined further.

Simplify first! 2√12 + 3√3 becomes 4√3 + 3√3 = 7√3 once you simplify √12 = 2√3.
Multiplying & Dividing Radicals
√a · √b = √(ab) √a / √b = √(a/b)

Multiply: Multiply the coefficients together and multiply the radicands together, then simplify the result.

Divide: Divide the coefficients, divide the radicands, simplify. If a radical remains in the denominator, rationalize it by multiplying numerator and denominator by √b.

Rationalize denominators: √a / √b = (√a · √b) / (√b · √b) = √(ab) / b.

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