Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 8 - Section 8.3 - Operations with Radicals - Exercise Set: 87

Answer

Perimeter=$4\sqrt3+4\sqrt5$ inches Area=$8+\sqrt{15}$ square inches

Work Step by Step

Perimeter is the sum of the lengths. For a square, $P=4s$. $P=4(\sqrt3+\sqrt5)$ Use the distributive property to simplify. $P=4\sqrt3+4\sqrt5$ The area of a square is the product of the length of 2 sides. $A=(\sqrt3+\sqrt5)(\sqrt3+\sqrt5)$ Use the FOIL method to multiply the two binomials. $A=(\sqrt3\times\sqrt3)+(\sqrt3\times\sqrt5)+(\sqrt3\times\sqrt5)+(\sqrt5\times\sqrt5)$ Use the product rule for square roots to simplify. $A=\sqrt9+\sqrt{15}+\sqrt{15}+\sqrt{25}$ Simplify square roots. Add like radicals. $A=3+2\sqrt{15}+5=8+\sqrt{15}$
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