The square root of 3 is an irrational number, which means it cannot be expressed as a fraction of two integers. It is the positive real number that, when multiplied by itself, gives the number 3. The square root of 3 can be expressed in different forms:

• Decimal form: The square root of 3 rounded up to 7 decimal places is 1.7320508.
• Radical form: The square root of 3 is denoted mathematically as √3.
• Exponent form: The square root of 3 is expressed as (3)½ or (3)0.5.

The square root of 3 is also known as Theodorus constant, after Theodorus of Cyrene, who proved its irrationality. It appears in algebraic expressions for various other trigonometric constants and has several geometric interpretations. For example, it is the leg length of an equilateral triangle that encompasses a circle with a diameter of 1. It is also the distance between parallel sides of a regular hexagon with sides of length 1 and the length of the space diagonal of a unit cube.

To find the value of the square root of 3, we can use different methods such as the long division method or approximations using continued fractions. The value of the square root of 3 is approximately equal to 1.7320508.