Rationalize the denominator. $$ \frac{\sqrt{7}}{\sqrt{10}} $$

Question

UpStudy AI · Accepted Answer

To **rationalize the denominator** of the expression

$$
\frac{\sqrt{7}}{\sqrt{10}},
$$

you need to eliminate the square root from the denominator. This can be achieved by multiplying both the numerator and the denominator by $$\sqrt{10}$$. Here's a step-by-step breakdown:

1. **Multiply Numerator and Denominator by $$\sqrt{10}$$:**

$$
\frac{\sqrt{7}}{\sqrt{10}} \times \frac{\sqrt{10}}{\sqrt{10}} = \frac{\sqrt{7} \times \sqrt{10}}{\sqrt{10} \times \sqrt{10}}
$$

2. **Simplify the Numerator and Denominator:**

- **Numerator:** $$\sqrt{7} \times \sqrt{10} = \sqrt{7 \times 10} = \sqrt{70}$$
  
- **Denominator:** $$\sqrt{10} \times \sqrt{10} = \sqrt{10^2} = 10$$

So, the expression becomes:

$$
\frac{\sqrt{70}}{10}
$$

3. **Final Answer:**

$$
\boxed{\dfrac{\sqrt{70}}{10}}
$$

This is the rationalized form of the original expression, with the denominator free of any square roots.
$$ \frac{\sqrt{70}}{10} $$

Rationalize the denominator.

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