What is the square root of 10?

The square root of 10 (√10) 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: √10 ≈ 3.16227766... Calculators give a decimal approximation, but this is only an approximation.

• Between which integers: It lies between 3 and 4, since 3² = 9 and 4² = 16.

• Simplified Radical Form: √10 is already in its simplest radical form. There are no perfect square factors of 10 that can be taken out.

• Relationship to other numbers: It can be expressed as √(2 x 5), highlighting its prime factorization.

• Geometric Interpretation: It represents the length of the diagonal of a rectangle with sides of length 1 and 3 (using the Pythagorean theorem: 1² + 3² = 10) or the side length of a square with area 10.

In short, while we can approximate its value, √10 is fundamentally an irrational number with an infinitely long, non-repeating decimal expansion.