What is the square root of 42?

The square root of 42 is an irrational number, meaning it cannot be expressed as an exact fraction or a finite decimal. To calculate or approximate the square root of 42:

1. **Understanding the value:**
The square root of 42 lies between two perfect squares:
- \( \sqrt{36} = 6 \)
- \( \sqrt{49} = 7 \)
So, \( 6 < \sqrt{42} < 7 \).

2. **Estimation using averages:**
To refine this estimate, take the midpoint of 6 and 7:
- Midpoint: \( \frac{6 + 7}{2} = 6.5 \).
- \( 6.5^2 = 42.25 \), which is slightly more than 42.
This means \( \sqrt{42} < 6.5 \).

Next, try another value slightly below 6.5, like 6.4:
- \( 6.4^2 = 40.96 \), which is less than 42.
So, \( 6.4 < \sqrt{42} < 6.5 \).

3. **Using approximation tools or calculators:**
With more precision, \( \sqrt{42} \approx 6.4807 \) (rounded to 4 decimal places).

4. **Final Answer:**
The square root of 42 is approximately 6.4807.