Questions: Simplify: 3 √[4]80 / √[4]5

Simplify: 3 √[4]80 / √[4]5
Transcript text: Simplify: \[ \frac{3 \sqrt[4]{80}}{\sqrt[4]{5}} \]
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Solution

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Solution Steps

To simplify the given expression, we can use the property of radicals that states \(\sqrt[n]{a} / \sqrt[n]{b} = \sqrt[n]{a/b}\). This allows us to combine the radicals into a single radical expression. Then, we can simplify the expression inside the radical.

Step 1: Combine the Radicals

We start by using the property of radicals: \[ \frac{3 \sqrt[4]{80}}{\sqrt[4]{5}} = 3 \cdot \frac{\sqrt[4]{80}}{\sqrt[4]{5}} = 3 \cdot \sqrt[4]{\frac{80}{5}} \]

Step 2: Simplify the Fraction Inside the Radical

Next, we simplify the fraction inside the radical: \[ \frac{80}{5} = 16 \] So the expression becomes: \[ 3 \cdot \sqrt[4]{16} \]

Step 3: Simplify the Fourth Root

We know that: \[ \sqrt[4]{16} = 2 \] Thus, the expression simplifies to: \[ 3 \cdot 2 = 6 \]

Final Answer

\[ \boxed{6} \]

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