( j ) A p p ly (jjjp 48. L o o k f o r a P a t t e r n From a viewing
height of h feet, the approximate
distance d to the horizon, in miles, is
given by the equation d = \/^-
a. To the nearest mile, what is the
distance to the horizon from a
height of 150 ft? 225 ft? 300 ft?
b. How does the distance to the horizon increase as the height increases?
- Think About a Plan A square picture on the front page of a newspaper occupies an
area of 24 in.2. What is the length of each side of the picture? Write your answer as a
radical in simplified form.- How can you find the side length of a square if you know the area?
- What property can you use to write your answer in simplified form?
Explain why each radical expression is or is not in simplified form.- ^13x
V4
51.
V3- -4V5 53. 5 V30
- Error Analysis A student simplified the radical expression at the right. What
mistake did the student make? What is the correct answer? - Reasoning You can simplify radical expressions with negative exponents by first
rewriting the expressions using positive exponents. What are the simplified forms
of the following radical expressions?
V3
YT3b.v-3
c. V5a^2
VlO a-1d.V(2 m)
m- Sports The bases in a softball diamond are located at the corners of a
3600-ft2 square. How far is a throw from second base to home plate? - Suppose a and b are positive integers.
a. Verify that if a = 18 and b = 10, then V a • Vb = 6 V5.
b. Open-Ended Find two other pairs of positive integers a and b such that
Va- Vb = 6V5.
Second
baseHome plateSimplify each radical expression.- Vl2 • V75 59. V26 • 2 60. V
Vo4 61.^=V£
,, 62. VIMy-
V3 63. ~VV 64. “ 3VV6
6S- V16nf
- V8 • VlO
- V20a2b3 67. V n 3h5c3 69.
Vi?
Solve each equation. Leave your answer in simplified radical form. - x2 + 6x - 9 = 0 71. n2 --2n + l= 5 72. 3y2 - 4y - 2 = 0
- Open-Ended What are three numbers whose square roots can be written in the
form a V3 for some integer value of al
624 Chapter 10 Radical Expressions and Equations