Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 10 - Section 10.4 - Adding, Subtracting, and Multiplying Radical Expressions - Exercise Set: 61

Answer

$(2\sqrt{7}+3\sqrt{5})(\sqrt{7}-2\sqrt{5})=-16-\sqrt{35}$

Work Step by Step

$(2\sqrt{7}+3\sqrt{5})(\sqrt{7}-2\sqrt{5})$ Evaluate the product: $(2\sqrt{7}+3\sqrt{5})(\sqrt{7}-2\sqrt{5})=2\sqrt{7^{2}}-4\sqrt{35}+3\sqrt{35}-6\sqrt{5^{2}}=...$ $...=2(7)-4\sqrt{35}+3\sqrt{35}-6(5)=...$ $...=14-4\sqrt{35}+3\sqrt{35}-30=...$ Simplify by combining like terms: $...=(14-30)+(3-4)\sqrt{35}=-16-\sqrt{35}$
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