Solve. √(w+3)=√(2 w-11)

Name: Problem 71, Chapter 10: Beginning and Intermediate Algebra
Uploaded: 2021-02-19T12:02:36-08:00
Duration: 1 min 1 s
Channel: Narayan Hari
Description: Solve. √(w+3)=√(2 w-11)

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Key Concepts

Cube Roots

Cube roots are a type of radical that find the number which, when raised to the third power, yields the original number. Unlike square roots, cube roots are defined for all real numbers since the cube of a negative number is also negative. This property is crucial when solving equations that involve cube roots, as it guarantees a unique solution due to their one-to-one nature.

Radical Equations

Radical equations are equations in which the variable appears under a radical, often necessitating the elimination of the radical to solve the equation. For cube roots, this can typically be achieved by raising both sides of the equation to the third power. Understanding how to properly manipulate and eliminate radicals is essential to solving these types of equations.

Algebraic Manipulation

Algebraic manipulation involves the rearrangement of equations, including operations such as adding, subtracting, multiplying, or raising both sides to a power, in order to isolate the variable. This fundamental skill in algebra is used to simplify equations and make the process of finding the solution more systematic and logical.

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