Like Radicals

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

$\sqrt{9}+\sqrt{16}$ is not $\sqrt{25}$ . The left side is 3 + 4 = 7. The right side is 5. You cannot add the numbers under the root signs.

You can add roots that are the same: $2\sqrt{3}+5\sqrt{3} = 7\sqrt{3}$ . It works like 2x + 5x = 7x. These are called like radicals. A root with no number in front counts as 1. Different roots, like $\sqrt{2}+\sqrt{3}$ , stay apart, like x and y.

Challenge

Simplify $4\sqrt{3}+2\sqrt{7}-\sqrt{3}+\sqrt{7}$ . Add the roots that are the same.

Try it yourself

4\sqrt{3}+2\sqrt{7}-\sqrt{3}+\sqrt{7}

Write it in simplest radical form

All lessons in Radicals & Rational Exponents

1Simplest Form

Perfect Square FactorsLike RadicalsSimplify 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 Root Distributing a Root Two 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