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Subtracting

Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 9 of 43.

Subtraction follows the same plan, with one thing to watch: a number already in front multiplies whatever comes out of the root. In 3√(28) - √(63), the root of 28 is 2√(7), so 3√(28) is 3 times that, 6√(7). The root of 63 is 3√(7).

3√(28) - √(63) = 6√(7) - 3√(7) = 3√(7)

The minus belongs to the whole second term, so all of its simplified form is taken away. The answer can even come out negative: √(8) - √(50) is 2√(2) - 5√(2), which is -3√(2).

Challenge

Simplify 5√(8) - √(18). Type each next line: first both terms simplified, with the 5 multiplied in, then the difference. The board accepts a line only if it equals the one above.

Try it yourself

5sqrt(8) - sqrt(18)

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 FirstSubtractingRecap: 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