What is the square root of 13?

The square root of 13 (√13) is an irrational number, meaning it cannot be expressed as a simple fraction and its decimal representation goes on forever without repeating.

Here's what we know about it:

• Approximate Value: √13 ≈ 3.60555... This is only an approximation; the decimal continues infinitely.

• Irrationality: As mentioned, it's irrational. This means you can't find two integers a and b such that √13 = a/ b.

• Location on the Number Line: It lies between 3 and 4, closer to 4.

• Calculation: It can be calculated using various methods, including numerical methods like the Babylonian method (or Heron's method) or Newton's method for finding roots. These iterative methods provide increasingly accurate approximations.

• Radical Form: Its simplest form is √13. It cannot be simplified further because 13 is a prime number.

In short, while we can approximate its value, √13 is fundamentally an irrational number that exists precisely as the square root of 13.