Rationalize the denominator: $$ \frac{21}{\sqrt{7}} $$

Question

UpStudy AI · Accepted Answer

To rationalize the denominator of the expression $$ \frac{21}{\sqrt{7}} $$, follow these steps:

1. **Multiply the numerator and the denominator by $$ \sqrt{7} $$** to eliminate the square root from the denominator:

$$
   \frac{21}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} = \frac{21\sqrt{7}}{(\sqrt{7})^2}
   $$

2. **Simplify the denominator**:

$$
   (\sqrt{7})^2 = 7
   $$

So the expression becomes:

$$
   \frac{21\sqrt{7}}{7}
   $$

3. **Simplify the fraction by dividing both the numerator and the denominator by 7**:

$$
   \frac{21\sqrt{7}}{7} = 3\sqrt{7}
   $$

**Final Answer:**
$$
3\sqrt{7}
$$
$$ 3\sqrt{7} $$

Rationalize the denominator: \( \frac{21}{\sqrt{7}} \)