What is the square root of 6?

The square root of 6 (√6) 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: √6 ≈ 2.44948974278... This is only an approximation; the decimal continues infinitely.

• Irrationality: As mentioned, it's irrational. This can be proven using a proof by contradiction similar to the proof for the irrationality of √2.

• Simplified Form: √6 cannot be simplified further because 6 has no perfect square factors other than 1. (e.g., √12 can be simplified to 2√3 because 12 = 4 * 3 and 4 is a perfect square).

• Relationship to other numbers: It's located between 2 and 3 on the number line, closer to 2. It's also related to other irrational numbers through multiplication and division. For example, √6 = √2 * √3.

• Geometric Interpretation: √6 represents the length of the diagonal of a rectangle with sides of length √2 and √3, or a rectangle with sides of length 1 and √6. It can also be related to various geometric constructions.

In short, √6 is a fundamental irrational number with a simple definition but an infinitely long and non-repeating decimal representation.