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 etc.3 4

Formal definition of “the square root of a”:

iff _____ba ab 2

* 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

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

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'

When an irrational number is written as a decimal, the decimal does not terminate nor repeat.

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.

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.

Examples: Simplify.

22

24

35

325 26

236

26

223

243

89

What’s wrong with the following simplification?

Neither 3 nor 6 is a perfect square.

2329

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.

Examples:

175

75

725

3512

Examples:

36

323

343

129

108

36

323

343

123

175

725

4925

7575

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.

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

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