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Chapter 10: Problem 47

Solve each equation. $$ \sqrt[4]{2 k-5}+4=0 $$

Short Answer

Expert verified
There is no real solution since the fourth root of a number cannot be negative.

Step by step solution

01

Isolate the Radical Expression

First, isolate the radical expression on one side of the equation. Subtract 4 from both sides of the equation: \[ \sqrt[4]{2k - 5} + 4 = 0 \] \[ \sqrt[4]{2k - 5} = -4 \]
02

Analyze the Radical Expression

Notice that a fourth root function must produce a non-negative result since the fourth root of a number cannot be negative. Therefore, the equation \( \sqrt[4]{2k - 5} = -4 \) has no real solution.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Fourth Roots
A fourth root of a number is a value that, when multiplied by itself four times, gives the original number. Mathematically, we express the fourth root of a number as \[ \frac{1}{4} \]. For example, the fourth root of 16 is 2, because \( 2 \times 2 \times 2 \times 2 = 16 \).
Isolating Radicals
Isolating the radical means getting the radical term by itself on one side of the equation. This simplifies the process of solving the equation. Let's break this down step by step.
No Real Solution
Sometimes, during the process of solving radical equations, you may encounter situations where no real solution exists.

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Most popular questions from this chapter

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