Honors Geometry Square Root Review. Square root is a subgroup of a larger group of numbers called...

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Honors Geometry Square Root Review

Transcript of Honors Geometry Square Root Review. Square root is a subgroup of a larger group of numbers called...

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.

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.

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.

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.

* 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.

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.

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.

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.

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.

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.

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.

What’s wrong with the following simplification?

Neither 3 nor 6 is a perfect square.

2329

Page 12: 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.

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.

Examples:

175

75

725

3512

Page 14: 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.

Examples:

36

323

343

129

108

36

323

343

123

175

725

4925

7575

Page 15: 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.

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.

Page 16: 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.

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

Page 17: 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.

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