what’s the square root of 58
What is the square root of 58?
Answer: The square root of 58 is an irrational number, meaning it cannot be expressed as a simple fraction and its decimal representation is non-repeating and non-terminating. To express this in a more precise form, you would typically turn to its decimal approximation.
Let’s calculate it:
\sqrt{58} \approx 7.615
This approximation can be extended to as many decimal places as necessary, such as:
\sqrt{58} \approx 7.61577310586 \ldots
For most practical purposes, a value of \approx 7.62 is often sufficient, but it depends on the required precision for your application.
Using a Calculator:
Modern calculators, including those on smartphones and computers, can quickly provide this approximation. Simply enter √58 or 58 √, depending on the calculator’s input method, and it will yield an accurate approximation.
Manual Calculation:
Alternatively, you can use methods like the Newton-Raphson method to iteratively approximate the square root. Here’s a quick overview of how this method works for \sqrt{58}:
- Start with a reasonable guess, say x_0 = 8.
- Apply the Newton-Raphson iteration formula:
x_{n+1} = \frac{x_n + \frac{58}{x_n}}{2}
- Repeat until the difference between successive values is smaller than your desired precision.
Applying this method:
- First iteration: x_1 = \frac{8 + \frac{58}{8}}{2} = 7.625
- Second iteration: x_2 = \frac{7.625 + \frac{58}{7.625}}{2} \approx 7.616
As you can see, after just a couple of iterations, we already get quite close to the actual square root.
In conclusion:
The square root of 58 is approximately 7.61577310586. For practical applications, you can round this value to whatever degree of precision you need.