Letters Under the Root
Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 4 of 43.
It is tempting to say √(x^2) is x. Try x = -3: then x^2 is 9, and the root of 9 is 3, not -3. The root is never negative, so it gives back x without its sign: √(x^2) = |x|.
That bar matters when you simplify. In √(12x^2), the square factor is 4x^2, which is (2x)^2. Split it off: √(4x^2) × √(3). The root of 4x^2 is |2x|, which is 2|x|, so the answer is 2|x|√(3).
Some powers need no bar. For a real x, √(x^4) is x^2, because x^2 is never negative already.
Challenge
Write √(50x^2) in simplest radical form. Type each next line: first a product of two roots, the first holding the whole square factor, number and letter together, then the simplified form. Write the absolute value with bars, as |x|. The board accepts a line only if it equals the one above.
Try it yourself
Write it in simplest radical form
Test yourselfThis 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 PowersPerfect Square FactorsThe Largest SquareLetters Under the RootCube RootsRecap: Simplifying Radicals7Powers and Roots Equations
Odd PowersEven PowersFractional PowersTwo Thirds PowerRecap: Power Equations