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Letters Under the Root

Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 5 of 40.

Is $\sqrt{{x}^{2}}$ always x? Try x = -3. $\left(-3\right)^2 = 9$ , and $\sqrt{9} = 3$ . The answer is 3, not -3.

A square root is never negative. So $\sqrt{{x}^{2}} = \left|x\right|$ . The bars mean absolute value: the size of x without its minus sign. Keep the bars when a letter comes out of a root: $\sqrt{12{x}^{2}} = \sqrt{4{x}^{2}}\cdot \sqrt{3} = 2\left|x\right|\sqrt{3}$ .

For $\sqrt{{x}^{4}} = {x}^{2}$ you need no bars. ${x}^{2}$ is never negative.

Challenge

Write $\sqrt{50{x}^{2}}$ in simplest form. First write it as two roots multiplied. Put the perfect square, number and letter together, in the first root. Write the absolute value with bars, as |x|.

Try it yourself

\sqrt{50x^{2}}

Write it in simplest radical form

All lessons in Radicals & Rational Exponents

1Simplest Form

Perfect Square Factors Like Radicals Simplify 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 RootCube 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