Basic Mathematics for College Students

Some other examples of radical expressions are:

To evaluate (or simplify) a radical expression like those shown above, we need to
find the positive square root of the radicand. For example, if we evaluate (read as
“the square root of 36”), the result is

because. 62  36

136  6

136

136 1100 1144 181

4.6 Square Roots 387

Caution! Remember that the radical symbol asks you to find only the

positivesquare root of the radicand. It is incorrect, for example, to say that

136 is 6 and  6

The symbol is used to indicate the negative square rootof a positive
number. It is the opposite of the positive square root. Since –6 is the negative square
root of 36, we can write

Read as “the negative square root of 36 is 6” or “the opposite of the
square root of 36 is 6.” represents the negative number whose
square is 36.
If the number under the radical symbol is 0, we have.
Numbers, such as 36 and 49, that are squares of whole numbers, are called perfect
squares.To evaluate square root radical expressions, it is helpful to be able to identify
perfect square radicands. You need to memorize the following list of perfect squares,
shown in red.

10  0

 136

 136  6

 1

Perfect Squares

9  32 49  72 121  112 225  152

4  22 36  62 100  102 196  142

1  12 25  52 81  92 169  132

0  02 16  42 64  82 144  122

A calculator is helpful in finding the square root of a perfect square that is larger
than 225.

EXAMPLE (^2) Evaluate each square root: a. b.
StrategyIn each case, we will determine what positive number, when squared,
produces the radicand.
WHYThe radical symbol indicates that the positive square root of the
number written under it should be found.
Solution
a. Ask: What positive number, when squared, is 81?
The answer is 9 because 9^2 81.
b. is the opposite (or negative) of the square root of 100. Since
, we have
 1100  10

1100  10

 1100

181  9

1

181  1100

Self Check 2

Evaluate each square root:

a.

b.

Now TryProblems 25 and 29

 181

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