Simplify First

Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 3 of 40.

$\sqrt{8}+\sqrt{18}$ has two different roots, but it is equal to $5\sqrt{2}$ . First simplify each root: $\sqrt{8} = 2\sqrt{2}$ and $\sqrt{18} = 3\sqrt{2}$ . Now both are roots of 2, so you can add them: 2 + 3 = 5.

If there is already a number in front, multiply it by the number that comes out: $3\sqrt{8} = 3\cdot 2\sqrt{2} = 6\sqrt{2}$ .

Challenge

Simplify $5\sqrt{8}-\sqrt{18}$ . First write both terms in simplest form, with the 5 multiplied in. Then subtract.

Try it yourself

5\sqrt{8}-\sqrt{18}

Write it in simplest radical form

All lessons in Radicals & Rational Exponents

1Simplest Form

Perfect Square Factors Like RadicalsSimplify FirstRecap: 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