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Chapter 0: Problem 101

Simplify by reducing the index of the radical. $$\sqrt[4]{5^{2}}$$

Short Answer

Expert verified
The expression \(\sqrt[4]{5^{2}}\) simplifies to \(\sqrt{5}\).

Step by step solution

01

Understand the radical

In the expression, \(\sqrt[4]{5^{2}}\), the 4 is the fourth root, meaning we will divide the exponent (in this case 2) by 4.
02

Perform the Operation

Divide the exponent (2) by the root (4). This gives you \(2/4 = 0.5\). This means that the expression simplifies to \(5^{0.5}\).
03

Convert the exponent

The exponent of \(0.5\) is equivalent to a square root. So, \(5^{0.5}\) is equivalent to \(\sqrt{5}\).

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Most popular questions from this chapter

Explain how to factor \(3 x^{2}+10 x+8\)

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Determine whether each statement makes sense or does not make sense, and explain your reasoning. I simplified the terms of \(2 \sqrt{20}+4 \sqrt{75},\) and then I was able to add the like radicals.

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