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Distributing a Root

Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 9 of 40.

A root in front of a bracket multiplies every term inside, exactly as a number does. Take $\sqrt{5}\left(\sqrt{10}+4\right)$ . The root of 5 times the root of 10 is $\sqrt{50}$ , and the root of 5 times 4 is $4\sqrt{5}$ :

$\sqrt{5}\left(\sqrt{10}+4\right) = \sqrt{50}+4\sqrt{5}$

Then simplify what you made: $\sqrt{50}$ is $5\sqrt{2}$ , so the answer is $5\sqrt{2}+4\sqrt{5}$ . The two terms have different roots, so they stay apart.

Challenge

Expand and simplify $\sqrt{3}\left(\sqrt{6}+2\right)$ . Leave every root in simplest form.

Try it yourself

\sqrt{3}\left(\sqrt{6}+2\right)

Write it in simplest radical form

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Radicals & Rational Exponents

1Simplest Form

Perfect Square Factors Like Radicals Simplify First Recap: Adding Radicals

4Rationalizing

One Root Below A Number and a Root The Conjugate Below Recap: Rationalizing

7Powers and Roots Equations

Odd Powers Even Powers Fractional Powers Two Thirds Power Recap: Power Equations

2Letters and Cube Roots

Letters Under the Root Cube Roots Recap: Simplifying Radicals

5Rational Exponents

One Over n m Over n Negative Exponents Exponent Rules Still Work Recap: Rational Exponents

8Radical Functions

Domain of a Root Evaluating Inverse of a Square Recap: Radical Functions

3Multiplying Radicals

Root Times RootDistributing a RootTwo Brackets Conjugate Pairs Recap: Multiplying Radicals

6Radical Equations

Square Both Sides Isolate the Root First A False Answer Cube Root Equations Recap: Radical Equations

9Final Challenges

Final: Simplify and Add Final: Clear the Root Final: The Exponent Final: Check It Final: The Falling Ball