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SQUARES & SQUARE ROOTS

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Squares Squares: “Squaring” a number means to raise a number to the second power. Example: 4² = 4 · 4 = 16 9² = 9 · 9 = 81 16² = 16 · 16 = 256

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Square Roots The Square Root of a number is the number you can multiply by itself to give you that number. Thus, = 2, because 22=4 = 3, because 32=9 Try: = 8, because 82=64 = 12, because 122=144 = 1, because 12 = 1 = 0, because 02 = 0

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**is a perfect square because = 7 49**

Perfect Squares A Perfect Square: is “perfect” because its square root is a whole number. Example: is a perfect square because = 7 49

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**is NOT a perfect square because = 6.3245… 40**

Non-Perfect Squares A Non-Perfect Square: is a number whose square root is NOT a whole number. Example: is NOT a perfect square because = … 40

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Approximating Square Roots You need to estimate its value of non-perfect squares by determining which two whole numbers it falls in between. Example: 11 is a non-perfect square 11 falls between perfect squares 9 & 16 Therefore, is between and Since, = 3 and = 4 Then is between 3 and 4

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**Find the two consecutive numbers the following non-perfect square fall between. SHOW WORK!**

√55 √23 √5 √14 √44 and Between 7 & 8 and Between 4 & 5 and Between 2 & 3 and Between 3 & 4 and Between 6 & 7

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**Answer the following problem SHOW WORK!**

I am a number. I am not zero. If I am squared, I’m still the same number. What number am I? 1

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**Answer the following problem SHOW WORK!**

If a square bedroom has an area of 144 square feet, what is the length of one wall? 12 feet 9

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**Answer the following problem SHOW WORK!**

An artist is making two stained-glass windows. One window has a perimeter of 48 inches. The other window has an area of 110 inches. Which window is bigger? The window with a perimeter of 48 inches. 10

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**Answer the following problem SHOW WORK!**

A square garden has an area of 225 square feet. How much fencing will a gardener need to buy in order to place fencing around the garden? 60 feet 11

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( + ) ÷ ( + ) = ( + ) ( – ) ÷ ( – ) = ( + ) Simplify the following. ( + ) ÷ ( – ) = ( – ) ( – ) ÷ ( + ) = ( – ) 1) – 54 ÷ ( – 9 )= 6 2) – 48 ÷ 6= – 8 3)

( + ) ÷ ( + ) = ( + ) ( – ) ÷ ( – ) = ( + ) Simplify the following. ( + ) ÷ ( – ) = ( – ) ( – ) ÷ ( + ) = ( – ) 1) – 54 ÷ ( – 9 )= 6 2) – 48 ÷ 6= – 8 3)

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