Multiplying and DIviding Radical Expressions **Task: Multiply**Given the expression: \((5 + \sqrt{3})(5 - \sqrt{3}) = \) [Box with the answer 22]**Explanation:**This expression is a difference of squares. It can be simplified by using the formula:\[(a + b)(a - b) = a^2 - b^2\]In this case, \(a = 5\) and \(b = \sqrt{3}\).Applying the formula:\[(5 + \sqrt{3})(5 - \sqrt{3}) = 5^2 - (\sqrt{3})^2 = 25 - 3 = 22\]The final answer is 22, which is placed in the answer box. **Problem Statement:**Divide. Show your work to receive full credit.\[\frac{2+\sqrt{2}}{2-\sqrt{3}}\]**Instructions:**To divide and simplify the expression given, you should multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of \(2 - \sqrt{3}\) is \(2 + \sqrt{3}\). **Steps:**1. Multiply both the numerator and the denominator by the conjugate of the denominator: \[ \frac{(2+\sqrt{2})(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3})} \]2. Expand both the numerator and the denominator: - **Numerator:** \( (2+\sqrt{2})(2+\sqrt{3}) = 4 + 2\sqrt{3} + 2\sqrt{2} + \sqrt{6} \) - **Denominator:** \( (2-\sqrt{3})(2+\sqrt{3}) = 4 - 3 = 1 \)3. Simplify the expression: Since the denominator is 1, the expression simplifies to the expanded numerator: \[ 4 + 2\sqrt{3} + 2\sqrt{2} + \sqrt{6} \]Thus, the division results in the simplified expression \(4 + 2\sqrt{3} + 2\sqrt{2} + \sqrt{6}\).

Answered: Multiplying and DIviding Radical…

Math

Algebra

Multiplying and DIviding Radical Expressions

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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