1 divided by the square root of 5 added to the square root of 68

To solve the given expression \( \frac{1}{\sqrt{5}} + \sqrt{68} \), follow these steps:

1. **Simplify each component separately:**

   - Calculate \( \sqrt{5} \):
     \[
     \sqrt{5} \approx 2.236
     \]
   
   - Calculate \( \sqrt{68} \):
     \[
     \sqrt{68} = \sqrt{4 \times 17} = 2\sqrt{17} \approx 8.246
     \]

2. **Evaluate the fraction \( \frac{1}{\sqrt{5}} \):**
   \[
   \frac{1}{\sqrt{5}} \approx \frac{1}{2.236} \approx 0.447
   \]

3. **Add the two results:**
   \[
   \frac{1}{\sqrt{5}} + \sqrt{68} \approx 0.447 + 8.246 \approx 8.693
   \]

Thus, the value of \( \frac{1}{\sqrt{5}} + \sqrt{68} \) is approximately \( 8.693 \).

Would you like more details or have any questions?

Here are 5 numbered questions you might ask next:
1. How do you rationalize the denominator in the expression \( \frac{1}{\sqrt{5}} \)?
2. What is the exact value of \( \sqrt{68} \)?
3. Can you show the step-by-step process of simplifying \( \sqrt{68} \)?
4. How do you approximate square roots manually?
5. What are some properties of square roots in algebra?

**Tip:** When approximating square roots, it can be helpful to know the squares of integers close to your number to get a better estimate.

Learn how to calculate the expression 1 divided by the square root of 5 added to the square root of 68 with a step-by-step solution. This problem involves evaluating square roots and adding fractions. Suitable for high school students.

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