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Like Radicals

Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 7 of 43.

2√(3) + 5√(3) works exactly like 2x + 5x. The root √(3) plays the part of x, so two of it plus five of it is seven of it: 7√(3). Roots with the same number under them are like radicals, and you add or subtract the numbers in front.

A root with no number in front has a 1 there. So 6√(7) - √(7) is 6 minus 1 of them, which is 5√(7).

Different roots do not combine, any more than x and y do. √(2) + √(3) is not √(5): the sum is about 3.15, while √(5) is about 2.24. The sum stays as it is.

Challenge

Simplify 3√(5) + 4√(5) - √(5). All three are like radicals, so type the result as the next line.

Try it yourself

3sqrt(5) + 4sqrt(5) - sqrt(5)

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 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 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