Questions: Rationalize the denominator and simplify. 8 / √5

Rationalize the denominator and simplify. 8 / √5
Transcript text: Rationalizing a denominator: Quotient involving square roots Rationalize the denominator and simplify. \[ \frac{8}{\sqrt{5}} \]
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Solution

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Solution Steps

Step 1: Identify the Problem

We need to rationalize the denominator of the fraction: \[ \frac{8}{\sqrt{5}} \]

Step 2: Multiply by the Conjugate

To rationalize the denominator, we multiply both the numerator and the denominator by \(\sqrt{5}\): \[ \frac{8}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}} \]

Step 3: Simplify the Expression

Perform the multiplication in the numerator and the denominator: \[ \frac{8 \cdot \sqrt{5}}{\sqrt{5} \cdot \sqrt{5}} = \frac{8\sqrt{5}}{5} \]

Final Answer

The rationalized form of the given expression is: \[ \boxed{\frac{8\sqrt{5}}{5}} \]

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