388 Chapter 4 Decimals
Caution! Radical expressions such asdo not represent real numbers, because there are no real numbers that when
squared give a negative number.
Be careful to note the difference between expressions such as and. We have seen that is a real number:. In contrast,
1 36 is not a real number.
1 36 136 136 6
136
1 36 1 100 1 144 1 81
Using Your CALCULATOR Finding a square root
We use the key (square root key) on a scientific calculator to find
square roots. For example, to find , we enter these numbers and press
these keys.
729
We have found that. To check this result, we need to square 27.
This can be done by entering 27 and pressing the key. We obtain 729. Thus,
27 is the square root of 729.
Some calculator models require keystrokes of and then followed
by the radicand to find a square root.2nd 1
x^21729 27
(^1 27)
1729
1
2 Find the square root of fractions and decimals.
So far, we have found square roots of whole numbers. We can also find square roots of
fractions and decimals.EXAMPLE 3
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.
Solutiona. Ask: What positive fraction, when squared, is?
The answer is because.b. Ask: What positive decimal, when squared, is 0.81?
The answer is 0.9 because (0.9)^2 0.81.1 0.810.9
1582
2
85 642525
B^6425
64
5
8
1
1 0.81
B
25
64
Self Check 3
Evaluate:a.b.Now TryProblems 37 and 431 0.04
B
16
49
3 Evaluate expressions that contain square roots.
In Chapters 1, 2, and 3, we used the order of operations rule to evaluate expressions
that involve more than one operation. If an expression contains any square roots, they
are to be evaluated at the same stage in your solution as exponential expressions. (See
step 2 in the familiar order of operations rule on the next page.)