Root Times Root
Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 11 of 43.
The rule √(ab) = √(a)√(b) also runs the other way: for numbers that are not negative, two roots multiplied make one root of the product. So √(2) × √(8) is √(16), which is 4. Neither root was a whole number, yet their product is.
The new root may need simplifying. √(6) × √(10) is √(60), and 60 holds the square 4:
√(6) × √(10) = √(60) = √(4) × √(15) = 2√(15)
Numbers in front multiply with each other, roots with roots: (2√(3))(4√(5)) is 8 times √(15). And a root times itself is what was under it: √(7) × √(7) is 7.
Challenge
Simplify √(6) × √(15). Type each next line: the product under one root, then that root split with its largest square, then the simplified form. 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 Equations3Multiplying Radicals
Root Times RootDistributing a RootTwo BracketsConjugate PairsRecap: Multiplying Radicals