Distributing a Root

Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 12 of 43.

A root in front of a bracket multiplies every term inside, exactly as a number does. Take √(5)(√(10) + 4). The root of 5 times the root of 10 is √(50), and the root of 5 times 4 is 4√(5):

√(5)(√(10) + 4) = √(50) + 4√(5)

Then simplify what you made: √(50) is 5√(2), so the answer is 5√(2) + 4√(5). The two terms have different roots, so they stay apart.

Challenge

Expand and simplify √(3)(√(6) + 2). Leave every root in simplest form.

Try it yourself

sqrt(3)(sqrt(6) + 2)

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

1Simplifying Radicals

Roots and Powers Perfect Square Factors The Largest Square Letters Under the Root Cube Roots Recap: Simplifying 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

2Adding & Subtracting Radicals

Like Radicals Simplify First Subtracting Recap: Adding 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