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: 88

Answer

Perimeter=$4\sqrt2+4\sqrt3$ inches $Area=$5+\sqrt{6}$ square inches

Work Step by Step

Perimeter is the sum of the lengths of the sides. For a square, $P=4s$. $P=4(\sqrt2+\sqrt3)$ Use the distributive property to simplify. $P=4\sqrt2+4\sqrt3$ The area of a square is the product of the length of 2 sides. $A=(\sqrt2+\sqrt3)(\sqrt2+\sqrt3)$ Use the FOIL method to multiply the two binomials. $A=(\sqrt2\times\sqrt2)+(\sqrt2\times\sqrt3)+(\sqrt2\times\sqrt3)+(\sqrt3\times\sqrt3)$ Use the product rule for square roots to simplify. $A=\sqrt4+\sqrt{6}+\sqrt{6}+\sqrt{9}$ Simplify square roots. Add like radicals. $A=2+2\sqrt{6}+3=5+\sqrt{6}$
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