Honors Geometry Square Root Review. Square root is a subgroup of a larger group of numbers called...
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![Page 1: Honors Geometry Square Root Review. Square root is a subgroup of a larger group of numbers called radicals (symbol: ) which include square roots and and.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649d9d5503460f94a8631d/html5/thumbnails/1.jpg)
Honors Geometry
Square Root Review
![Page 2: Honors Geometry Square Root Review. Square root is a subgroup of a larger group of numbers called radicals (symbol: ) which include square roots and and.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649d9d5503460f94a8631d/html5/thumbnails/2.jpg)
Square root is a subgroup of a larger group of numbers called
radicals (symbol: ) which include square roots and and etc.3 4
![Page 3: Honors Geometry Square Root Review. Square root is a subgroup of a larger group of numbers called radicals (symbol: ) which include square roots and and.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649d9d5503460f94a8631d/html5/thumbnails/3.jpg)
Formal definition of “the square root of a”:
iff _____ba ab 2
![Page 4: Honors Geometry Square Root Review. Square root is a subgroup of a larger group of numbers called radicals (symbol: ) which include square roots and and.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649d9d5503460f94a8631d/html5/thumbnails/4.jpg)
* Note that since , both 7 and –7 are square roots of 49. In geometry, the square root will represent the length of a segment, which is always positive. Consequently, we will only use the positive square root of a number.
________ because ____49 ________ because ____36
497 2
7 4972 6 3662
![Page 5: Honors Geometry Square Root Review. Square root is a subgroup of a larger group of numbers called radicals (symbol: ) which include square roots and and.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649d9d5503460f94a8631d/html5/thumbnails/5.jpg)
Any number whose square root is a whole number, such as the examples above, is called a perfect square.
Complete the list of the first 15 perfect squares.1,4,9,16,25, ,36 ,49 ,64 ,81 ,100 ,121 ,144 ,169 ,196 ,225
![Page 6: Honors Geometry Square Root Review. Square root is a subgroup of a larger group of numbers called radicals (symbol: ) which include square roots and and.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649d9d5503460f94a8631d/html5/thumbnails/6.jpg)
The square root of any whole number that is not a perfect square will be an irrational number.
An irrational number is a number that
fraction. a as written bet can'
![Page 7: Honors Geometry Square Root Review. Square root is a subgroup of a larger group of numbers called radicals (symbol: ) which include square roots and and.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649d9d5503460f94a8631d/html5/thumbnails/7.jpg)
When an irrational number is written as a decimal, the decimal does not terminate nor repeat.
![Page 8: Honors Geometry Square Root Review. Square root is a subgroup of a larger group of numbers called radicals (symbol: ) which include square roots and and.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649d9d5503460f94a8631d/html5/thumbnails/8.jpg)
On quizzes and tests, you must always give an exact answer unless
you are told to round. If your answer involves a square root, you
must always simplify the square root.
![Page 9: Honors Geometry Square Root Review. Square root is a subgroup of a larger group of numbers called radicals (symbol: ) which include square roots and and.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649d9d5503460f94a8631d/html5/thumbnails/9.jpg)
To simplify a square root, you must “factor out” any perfect square factor
(other than 1) in the radicand (the number under the radical sign). When simplifying a square root, that is not a perfect square, you will not eliminate the square root entirely. The goal is to
make the radicand as small as possible.
![Page 10: Honors Geometry Square Root Review. Square root is a subgroup of a larger group of numbers called radicals (symbol: ) which include square roots and and.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649d9d5503460f94a8631d/html5/thumbnails/10.jpg)
Examples: Simplify.
22
24
35
325 26
236
26
223
243
89
![Page 11: Honors Geometry Square Root Review. Square root is a subgroup of a larger group of numbers called radicals (symbol: ) which include square roots and and.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649d9d5503460f94a8631d/html5/thumbnails/11.jpg)
What’s wrong with the following simplification?
Neither 3 nor 6 is a perfect square.
2329
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If a problem involves multiplying square roots, you simply multiply the whole numbers and multiply
the radicands. You can never multiply a whole number times a
radicand.
![Page 13: Honors Geometry Square Root Review. Square root is a subgroup of a larger group of numbers called radicals (symbol: ) which include square roots and and.](https://reader036.fdocuments.us/reader036/viewer/2022082505/56649d9d5503460f94a8631d/html5/thumbnails/13.jpg)
Examples:
175
75
725
3512
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Examples:
36
323
343
129
108
36
323
343
123
175
725
4925
7575
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In the same way that addition is the inverse operation of
subtraction and multiplication is the inverse operation of division,
taking the square root is the inverse operation of squaring a
number.
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Solve each equation for x. Round your answers to the nearest 1000th.
Technically (like in Algebra II next year), when you introduce the square root into a problem, you must consider both the positive and negative square root that can result. But as I mentioned earlier, here in geometry, we will consider only the positive value.
5
25
252
x
x
x
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Solve each equation for x. Round your answers to the nearest 1000th.
483.7
56
56
81252
2
x
x
x
x
165.9
84
84
21632
2
x
x
x