Roots That Are Not Whole
Part of the Factoring & Quadratics section of Coddy's Algebra journey. Lesson 46 of 63.
No whole number squares to 5, but x^2 = 5 still has two solutions. They are written with the square root sign: x = ±√5. These are the exact numbers whose square is 5.
The number √5 lies between √4 = 2 and √9 = 3. It is approximately 2.236. Keep √5 when you want an exact answer. Use a decimal only when an approximation is asked for.
For x^2 = a with a positive number a, the solutions are x = ±√a. If a is a perfect square, the solutions are whole numbers. If not, keep the square root sign in the answer, or give a decimal approximation when it is asked for.
Challenge
EasySolve x^2 = 13. Give the exact answer.
Try it yourself
Solve for x
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Factoring & Quadratics
1What Factoring Is
Two DirectionsThe Reverse GearUn-Distributing LettersThe Check Is MultiplicationRecap: First Factors4Minus Signs in the Machine
A Negative ProductWhich One Gets the MinusBoth NegativeThe Sign MapRecap: Signs2The Greatest Common Factor
Number and Letter TogetherThe Largest OneHigher PowersThree Terms Share TooRecap: The GCF5Special Shapes
A Missing MiddleThe Shape in LettersThe Perfect SquareThe Minus VersionPrime PolynomialsRecap: Special Shapes3The Sum-Product Machine
Reading the ProductHunting the PairThe Machine in LettersLonger HuntsRecap: The Machine6Factor Completely
Two LayersSquares InsideCompletely Means CompletelyThe Deep CheckRecap: Factor Completely9The Square Root Method
Undoing a SquareArrange, Then RootA Squared PackageRoots That Are Not WholeRecap: Square Roots