Menu

English

Simplify First

Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 8 of 43.

√(28) + √(63) looks like two different roots, so it seems nothing combines. Simplify each one first: √(28) is 2√(7) and √(63) is 3√(7). Now they are like radicals, and the sum is 5√(7).

That is why simplest form matters: two roots that look unrelated can turn out to be multiples of the same root. Never decide that roots are unlike until each one is simplified.

Challenge

Simplify √(12) + √(27). Simplify each root, then collect.

Try it yourself

sqrt(12) + sqrt(27)

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 RadicalsSimplify FirstSubtracting 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 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