Solve. √(2 c+3)=√(5 c)

Name: Problem 21, Chapter 10: Beginning and Intermediate Algebra
Uploaded: 2020-06-27T17:50:23-08:00
Duration: 26 s
Channel: Amy Jiang
Description: Solve. √(2 c+3)=√(5 c)

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Key Concepts

Squaring Both Sides

A common method for solving square root equations is to square both sides of the equation. This step eliminates the square roots and transforms the equation into a polynomial or linear equation that is easier to solve. However, this operation may introduce solutions that are not valid for the original equation.

Extraneous Solutions

Extraneous solutions are potential answers that arise after squaring both sides of an equation but do not satisfy the original equation. It is essential to substitute all obtained solutions back into the original equation to verify their validity and discard any extraneous ones.

Square Root Equations

These are equations that include a variable inside a square root. Such equations require careful handling because the operations on a square root function are valid only when the radicand (the expression inside the square root) is non-negative in the set of real numbers.

Domain Restrictions

When solving square root equations, it is important to consider that the expression inside each square root must be greater than or equal to zero to ensure that the square root is defined in the real numbers. These restrictions can influence the set of possible solutions.

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