Powers and roots

• A “perfect” number is the product when you raise a whole number to a ______ (or multiply a number by itself multiple times)

• Powers and roots _____ each other Perfect Squares

𝑥!

Square Roots

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Perfect Cubes

𝑥!

Cube Roots

𝑥!

1! = 1 1 = 1 1! = 1 1! = 1 2! = 4 4 = 2 2! = 8 8! = 2 3! = 9 9 = 3 3! = 27 27! = 3 4! = 16 16 = 4 4! = 64 64! = 4 5! = 25 25 = 5 5! = 125 125! = 5 6! = 36 36 = 6 6! = 216 216! = 6 7! = 49 49 = 7 7! = 343 343! = 7 8! = 64 64 = 8 8! = 512 512! = 8 9! = 81 81 = 9 9! = 729 729! = 9 10! = 100 100 = 10 10! = 1000 1000! = 10 11! = 121 121 = 11 11! = 1331 1331! = 11 12! = 144 144 = 12 12! = 1728 1728! = 12 13! = 169 169 = 13 13! = 2197 2197! = 13

Estimating non-perfect Roots You can estimate where a non-perfect root will land on the number line by estimating the two ______________ (back to back) whole numbers that it falls between. Examples Find the two consecutive whole numbers each root falls between. ____ = ___ 24 ____ = ___ ____ = ___ 84 ____ = ___ ____ = ___ 75! ____ = ___ ____ = ___ 450! ____ = ___

Powers and roots

• A “perfect” number is the product when you raise a whole number to a ______ (or multiply a number by itself multiple times)

• Powers and roots _____ each other Perfect Squares

𝑥!

Square Roots

𝑥

Perfect Cubes

𝑥!

Cube Roots

𝑥!

1! = 1 1 = 1 1! = 1 1! = 1 2! = 4 4 = 2 2! = 8 8! = 2 3! = 9 9 = 3 3! = 27 27! = 3 4! = 16 16 = 4 4! = 64 64! = 4 5! = 25 25 = 5 5! = 125 125! = 5 6! = 36 36 = 6 6! = 216 216! = 6 7! = 49 49 = 7 7! = 343 343! = 7 8! = 64 64 = 8 8! = 512 512! = 8 9! = 81 81 = 9 9! = 729 729! = 9 10! = 100 100 = 10 10! = 1000 1000! = 10 11! = 121 121 = 11 11! = 1331 1331! = 11 12! = 144 144 = 12 12! = 1728 1728! = 12 13! = 169 169 = 13 13! = 2197 2197! = 13

Estimating non-perfect Roots You can estimate where a non-perfect root will land on the number line by estimating the two ______________ (back to back) whole numbers that it falls between. Examples Find the two consecutive whole numbers each root falls between. ____ = ___ 24 ____ = ___ ____ = ___ 84 ____ = ___ ____ = ___ 75! ____ = ___ ____ = ___ 450! ____ = ___