# What is the square root of 3

The square root of 3 is a number that, when multiplied by itself, equals 3. In other words, it is a number that, when squared, equals 3.

## What is the square root of 3

The square root of 3 is denoted by the symbol √3 and is approximately equal to 1.7320508075688772935274463415059. This number is an irrational number, which means that it cannot be represented as a simple fraction and has an infinite number of decimal places.

The square root of 3 has many interesting properties. For example, it is the hypotenuse of a right triangle with sides of length 1 and 2 (a 3-4-5 triangle). It is also the radius of a circle with area equal to 3.

In mathematics, the square root of 3 is an important number that appears in many different areas of study, including geometry, trigonometry, and algebra. It is often used in calculations and problem-solving, and it has many practical applications in the real world.

## How to find the value root of 3?

The value of the square root of 3 (√3) is approximately 1.7320508075688772935274463415059. It is an irrational number, which means that it cannot be expressed exactly as a fraction or a decimal with a finite number of digits.

To find the square root of 3, you can use a calculator or a math software program. You can also use the long division method or the Newton-Raphson method to approximate the value of the square root of 3.

Here is an example of how to find the square root of 3 using the long division method:

• Divide 3 by 2 to get 1.5.
• Write 1 as the first digit of the answer and place a bar over it.
• Multiply 1 by 2 to get 2. Write 2 under 3 and subtract it to get 1.
• Bring down the next digit (there is no next digit in this case) and place a bar over it.
• Divide 1 by 2 to get 0.5. Write 0 as the next digit of the answer.
• Multiply 0.5 by 2 to get 1. Write 1 under 1 and subtract it to get 0.
• Bring down the next digit (there is no next digit in this case) and place a bar over it.
• Divide 0 by 2 to get 0. Write 0 as the next digit of the answer.
• The answer is approximately 1.7320508075688772935274463415059, but you can continue the process to get a more accurate approximation.

Alternatively, you can use the Newton-Raphson method to find the square root of 3. This method involves iteratively improving an initial guess for the square root using the formula xn+1 = (xn + 3/xn)/2, where xn is the current guess and xn+1 is the next guess. You can start with an initial guess of 1 and repeat the process until you get a result that is accurate enough for your needs.