squares & square roots. squares: “squaring” a number means to raise a number to the second...
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![Page 1: SQUARES & SQUARE ROOTS. Squares: “Squaring” a number means to raise a number to the second power. Example: 4² = 4 · 4 = 16 9² = 9 · 9 = 81 16² = 16 ·](https://reader036.vdocuments.mx/reader036/viewer/2022062409/56649cb75503460f9497cb86/html5/thumbnails/1.jpg)
SQUARES
&
SQUARE ROOTS
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•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
Squares
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Square RootsThe 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=9Try:
= 8, because 82=64
= 12, because 122=144
= 1, because 12 = 1
= 0, because 02 = 0
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A Perfect Square: is “perfect” because its square root is a whole number.Example:
is a perfect square because = 7
Perfect Squares
49
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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 = 6.3245…
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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√55
√23
√5
√14
√44
Find the two consecutive numbers the following non-perfect square fall between.
SHOW WORK!andandandandand
Between 7 & 8 Between 4 & 5 Between 2 & 3 Between 3 & 4 Between 6 & 7
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Answer the following problem SHOW WORK!
1. 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!
2. If a square bedroom has an area of 144 square feet, what is the
length of one wall?
12 feet
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Answer the following problem SHOW WORK!
3. 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.
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Answer the following problem SHOW WORK!
4. 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