A Number and a Root
Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 17 of 43.
Often the bottom holds a number and a root, as in 5/(3√(2)). Only the root is a problem: 3 is already a whole number. So multiply the top and the bottom by √(2) alone:
5/(3√(2)) = (5√(2))/(3 × 2) = (5√(2))/6
The bottom is 3 times √(2) × √(2), and that product is 2, so the bottom is 6. Multiplying by the whole 3√(2) also clears the root, but it drags an extra 3 along: you get (15√(2))/18 and then have to cancel the 3 back out.
After rationalizing, look for a common factor between the number on top and the bottom. In 7/(2√(7)), multiplying by √(7) gives (7√(7))/14, and 7 over 14 cancels to leave √(7)/2.
Challenge
Write 3/(2√(6)) with no root in the denominator, then simplify it. Use the move chips.
Try it yourself
Clear the root from the denominator
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