Basic Mathematics for College Students

390 Chapter 4 Decimals

Solution

Do the subtraction within the

parentheses.

Within the brackets, evaluate the

exponential expression and the

square root.

Do the multiplication within the

brackets.

Do the subtraction within the

brackets.

Do the multiplication.

 15 Do the addition.

 12 (27)

 12 3[9]

 12 3[918]

 12 3[93(6)]

12  3 C 32 ( 4  1 ) 136 D 12  3 C 32  3136 D

4 Evaluate formulas involving square roots.

To evaluate formulas that involve square roots, we replace the letters with specific

numbers and the then use the order of operations rule.

EXAMPLE (^7) Evaluate for and.
StrategyIn the given formula, we will replace the letter awith 3 and bwith 4.
Then we will use the order of operations rule to find the value of the radicand.
WHYWe need to know the value of the radicand before we can find its square
root.
Solution
This is the formula to evaluate.
Replace awith 3 and bwith 4.
Evaluate the exponential expressions.
Do the addition.
 5 Evaluate the square root.

 125

 19  16

 232  42

c 2 a^2 b^2

c 2 a^2 b^2 a 3 b 4

Self Check 7

Evaluate for

and.

Now TryProblem 81

c 17 b 15

a 2 c^2 b^2

5 Approximate square roots.

In Examples 2–7, we have found square roots of perfect squares. If a number is not a

perfect square, we can use the key on a calculator or a table of square roots to

find its approximatesquare root. For example, to find using a scientific calculator,

we enter 17 and press the square root key:

The display reads

4.123105626

This result is an approximation, because the exact value of is a nonterminating

decimalthat never repeats. If we round to the nearest thousandth, we have

Read as “is approximately equal to.”

To check this approximation, we square 4.123.

Since the result is close to 17, we know that 117 4.123.

(4.123)^2 16.999129

117 4.123

117

17 1

117

1

n

11 3.317

12 3.464

13 3.606

14 3.742

15 3.873

16 4.000

17 4.123

18 4.243

19 4.359

20 4.472

1 n