Radical Operations

Explore like radical addition, multiplying radicals, division and restrictions.

Lesson 3 of 53 parts Practice Flashcards

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Like Radical Addition

Objective: Explain like radical addition and use it to solve or interpret a problem.

Only terms with the same simplified radicand and root index can combine by adding coefficients. No, their radicands differ.

Worked examples

Try itRadical Operations — practice 1.1: Combine 3√5 + 7√5. What is the coefficient of √5?Show answer

Step 1: The radicals have the same radicand 5. Step 2: Add their coefficients 3+7. Step 3: The coefficient is 10.

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Like Radical Addition

Objective: Explain like radical addition and use it to solve or interpret a problem.

Only terms with the same simplified radicand and root index can combine by adding coefficients. No, their radicands differ.

Worked examples

Try itRadical Operations — practice 1.1: Combine 3√5 + 7√5. What is the coefficient of √5?Show answer

Step 1: The radicals have the same radicand 5. Step 2: Add their coefficients 3+7. Step 3: The coefficient is 10.

Multiplying Radicals

Objective: Explain multiplying radicals and use it to solve or interpret a problem.

Multiply under one root when real-domain conditions permit, then simplify perfect powers; distribution applies across sums of radical terms. The new radicand may contain extractable perfect powers.

Worked examples

Try itRadical Operations — practice 2.1: Find √16·√64 for positive a and c.Show answer

Step 1: √16=4. Step 2: √64=8. Step 3: Multiply to get 32.

Division and Restrictions

Objective: Explain division and restrictions and use it to solve or interpret a problem.

A radical denominator must be nonzero; rationalizing a denominator may change appearance while preserving value on the valid domain. Zero in any denominator makes the original expression undefined.

Worked examples

Try itRadical Operations — practice 3.1: Compute √484/√4 for positive a,c.Show answer

Step 1: The principal roots are 22 and 2. Step 2: Divide 22/2. Step 3: The quotient is 11.

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