Algebra 1

Published by Prentice Hall

Chapter 10 - Radical Expressions and Equations - 10-2 Simplifying Radicals - Practice and Problem-Solving Exercises - Page 610: 35

Answer

x = $\sqrt 26 w$

Work Step by Step

Since the triangle is a right angle triangle we use the pythagorean theorem. $a^{2} + b^{2} = c^{2}$ In this problem a=5w, b=w and c= x $(5w)^{2} + (w)^{2} = x^{2}$ $5w \times 5w + (w)^{2} = x^{2}$ $25w^{2} + w^{2} = x^{2}$ $26w^{2} = x^{2}$ We take square root of both sides $\sqrt (26w^{2}) = \sqrt x^{2}$ $\sqrt 26 w$ = x Therefore x = $\sqrt 26 w$

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