MATH TERMS FOR SQUARES AND SQUARE ROOTS

Square: the result of a number multiplied by itself (ex. (1.5)² = 1.5 × 1.5 = 2.25)
Perfect Square: the square of a whole number (ex. 3² = 3 × 3 = 9)
Square Root (sqrt): the inverse of squaring a number (ex. √25 = 5 )
Term: the number under the square root sign (ex. in √9, 9 is the term)

RULES FOR SQUARE AND SQUARE ROOT PROBLEMS (1)

                                        Multiple Roots with One Term                                         One Root with Multiple Terms

Addition                        Solve square root , then add                                                 Add terms, then solve square root
                                        [ex. √9 + √4 = 3 + 2 = 5]                                                         [ex. √(9 + 7) = √16 = 4]

Subtraction                 Solve square root , then subtract                                           Subtract terms, then solve square root
                                       [ex. √9 - √4 = 3 - 2 = 1]                                                            [ex. √(9 - 5) = √4 = 2]

Multiplication              Combine square roots, then multiply terms                          Multiply terms, then solve square root
                                       [ex. (√16)(√4) = √(16 × 4) = 8]                                                [ex. √(9 × 9) = √81 = 9]

Division                       Combine square roots, then divide terms                             Perform operation under square root, then divide
                                       [ex. √9 ÷ √3 = √(9 ÷ 3) = √3]                                                   [ex. √(4 + 5) ÷ √(11 - 2) = 1]

RULES FOR SQUARE AND SQUARE ROOT PROBLEMS (2)
                                        

                                        Multiple Roots with One Term                                         One Root with Multiple Terms

Addition                        Add the outsides, keep the square root                               -------------------------------------------
                                        [ex. 3√3 + 2√3 = 5√3]                                                         

Subtraction                 Subtract the outsides, keep the square root                         -------------------------------------------
                                       [ex. 4√3 - 2√3 = 2√3]                                                           

Multiplication              Multiply the outsides and insides, then multiply results        Factor terms, then solve simple squares
                                       [ex. 2√3 × 2√3 = 4√9 = 12]                                                     [ex. √45 = (√9)(√5) = 3√5]

Division                       Keep square roots, divide the outsides                                 Factor terms, then simplify using division
                                       [ex. 6√3 ÷ 2√3 = 3√3]                                                              [ex. √8 ÷ √2 = (√4 × √2) ÷ √2 = 2√2 ÷ √2 = 2 ]

Math: Square Root Practice

Lesson Includes:

— Math Terms for Squares and Square Roots

—Rules for Squares and Square Roots I

—Rules for Squares and Square Roots II

—Practice Questions

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SQUARE AND SQUARE ROOTS MATH QUIZ

 

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