Page 358 - Basic College Mathematics with Early Integers

S E C T I O N 4.6 I SQUARE ROOTS AND THE PYTHAGOREAN THEOREM 335

Example 9 Finding the Dimensions of a Park PRACTICE 9
A football field is a rectangle
An inner-city park is in the shape of a square that measuring 100 yards by 53
measures 300 feet on a side. A sidewalk is to be yards. Draw a diagram and find
constructed along the diagonal of the park. Find the length of the diagonal of a
the length of the sidewalk rounded to the nearest football field to the nearest
? 300 ft
whole foot. yard.
Solution: The diagonal is the hypotenuse of a
300 ft
right triangle, so we use the formula
2 2
hypotenuse = 21leg2 + 1other leg2
Putting the known values into the formula we have
2 2
hypotenuse = 213002 + 13002 The legs are both 300 feet.
= 290,000 + 90,000
= 2180,000
L 424 From Appendix A.6 or a calculator

The length of the sidewalk is approximately 424 feet.
Work Practice 9

Calculator Explorations Finding Square Roots

To simplify or approximate square roots using a calcula- Is this answer reasonable? Since 10 is between perfect
tor, locate the key marked 1 . squares 9 and 16, 210 is between 29 = 3 and 216 = 4.
To simplify 264, for example, press the keys Our answer is reasonable since 3.162 is between 3 and 4.

64 1 or 1 64 Simplify.
The display should read 8 .Then 1. 21024

264 = 8 2. 2676

To approximate 210, press the keys Approximate each square root. Round each answer to the
nearest thousandth.
10 1 or 1 10
3. 231
The display should read 3.16227766 . This is an
4. 219
approximation for 210. A three-decimal-place approxi-
5. 297
mation is
6. 256
210 L 3.162

Answer
9. 113 yd