Problem 101 - College Algebra

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: 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 \(5^{0.5}\).

Step 3: Convert the exponent

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