Undoing a Square
Part of the Numbers & Operations section of Coddy's Pre-Algebra journey. Lesson 41 of 60.
Squaring takes 7 to 49. The square root goes back the other way: it asks which number, squared, gives 49. The answer is 7, written √(49) = 7. The sign √ is the root sign, and the number under it is the one you start from.
Every perfect square has a whole number as its root: √(81) = 9 because 9^2 = 81, and √(25) = 5. To check a root, square it and see that you land back on the number under the sign. And although -7 squared is also 49, the root sign never gives a negative number, so √(49) is 7 and only 7.
In a longer line, each root becomes its number first: √(81) - √(25) becomes 9 - 5, which is 4.
Challenge
Work out √(121) - √(64).
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Numbers & Operations
1Working on the Board
Your First AnswerType the Next LineOne Line at a TimeDots and BarsFriendly ProductsRecap: Board Work4Adding Integers
Adding Two NegativesDifferent SignsZero PairsAdding Several IntegersRecap: Adding Integers2Order of Operations
Multiply Before AddingLeft to RightParentheses FirstBrackets Inside BracketsThe Fraction Bar GroupsRecap: Order of Operations5Subtracting Integers
Add the OppositeSubtracting a NegativePlus and Minus in a RowDistance Between NumbersRecap: Subtracting Integers8Square Roots
Perfect SquaresUndoing a SquareRoots in ExpressionsThe Root Sign GroupsBetween Two Whole NumbersRecap: Square Roots