step 1 So if we see this question, we have cube roots on both sides. So let us cube on both sides. Then

√(2 m-1)=√(m+13)

Name: Problem 55, Chapter 7: Algebra for College Students
Uploaded: 2022-02-26T19:42:47-08:00
Duration: 42 s
Channel: Vivek Kumar
Description: √(2 m-1)=√(m+13)

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Key Concepts

Cube Root Function

The cube root function returns the unique real number whose cube equals the given value. It is defined for all real numbers and is one-to-one, meaning that if the cube roots of two numbers are equal, then the numbers themselves are equal, which is a key property used when solving equations involving cube roots.

Radical Equations

Radical equations are equations in which the unknown variable appears under a radical sign. Solving these equations generally involves isolating the radical expression and then eliminating the radical by raising both sides of the equation to the power that matches the root, followed by solving the resulting equation.

Eliminating Radicals by Exponentiation

A common method for solving radical equations is to eliminate the radical by exponentiating both sides of the equation by the reciprocal of the root. In the case of cube roots, cubing both sides of the equation removes the radical, simplifying the equation into a standard form that can be readily solved.

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