Square Both Sides
Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 25 of 43.
A square undoes a square root: (√(9))^2 is 9, because √(9) is by definition the number whose square is 9. So when x is stuck under a root, square both sides of the equation and the root is gone.
Take √(x - 3) = 5. Squaring the left leaves x - 3, and squaring the right gives 25. So x - 3 = 25, and x is 28. Check it in the original: √(28 - 3) is √(25), which is 5.
On the board the move is Square both sides. Squaring can bring in an answer that does not work (you will meet one two lessons from now), so afterwards the board asks you to Check the answer in the original equation before it counts. A root also tells you something at a glance: √(x) = -2 has no solution at all, because a square root is never negative.
Challenge
Solve √(x + 5) = 4. Square both sides, finish the equation, then check your answer in the original equation.
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 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 Radicals6Radical Equations
Square Both SidesIsolate the Root FirstA False AnswerCube Root EquationsRecap: Radical Equations