2. We say that an element z E F is a square root of a E F whenever 2² = a, we denote the square root of a as √a. It can be shown that in every nonnegative element in a complete ordered field has a unique nonnegative square root. In a complete ordered field with a, b, c, d E F, show the following: (a) a ≤ √a²; (b) Suppose that a and b are nonnegative, then Vab = √a√b; (c) √(a + c)² + (b + d)² ≤ √a² + b² + √²² + ď².

2. We say that an element z E F is a square root of a E F whenever 2² = a, we denote the square root of a as √a. It can be shown that in every nonnegative element in a complete ordered field has a unique nonnegative square root. In a complete ordered field with a, b, c, d E F, show the following: (a) a ≤ √a²; (b) Suppose that a and b are nonnegative, then Vab = √a√b; (c) √(a + c)² + (b + d)² ≤ √a² + b² + √²² + ď².

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.1: Real Numbers

Problem 36E

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