Roots in Expressions
Part of the Numbers & Operations section of Coddy's Pre-Algebra journey. Lesson 42 of 60.
A root is worked out before the products and sums around it, just as a power is. In 3 × √(25) + 2 the root goes first: √(25) is 5, so the line becomes 3 × 5 + 2. Then the multiplication, 15 + 2, and last the sum, 17.
Notice how the board writes 3 × √(25): the 3 sits right against the root sign with no dot, the same way 3(2 + 4) meant 3 times the package. It means 3 times √(25). It is not the third root of 25, which would have a small raised 3 tucked into the sign, and the 3 does not go under the sign either.
Why the root first? The 3 is waiting to multiply a number, and until you take the root, you do not know which number that is. The root sign works like a package around 25 that must be opened before it can be used.
Challenge
Work out 5 × √(16) - 7, one step per line.
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