# Value of Root 3

The value of root 3 is a positive real number when it is multiplied by itself; it gives the number 3. It is not a natural number but a fraction. The square root of 3 is denoted by √3. The square root basically, gives a value which, when multiplied by itself gives the original number. Hence, it is the root of the original number.

To find the square root of any real number, without using a calculator, we need to check first if the number under the root is a perfect square or not. If a number is a perfect square, then we can easily find its square root using prime factorisation method. For example, the square root of 4 is ±2, since 22 = 4. But, here 3 is an imperfect square or a non-perfect square. Hence, we cannot use the factorisation method. Instead, we will be using the long division method to find the value of the square root of 3. The actual value of √3 is given below.

 Value of root 3, √3 =1.732

## Root 3 Value in Maths

In Maths, we used to calculate the square root values of many numbers. Some numbers are perfect squares, but some are non-perfect. We can calculate the root of perfect squares easily by just the factorisation method but to find the root of non-perfect squares, we have to use the long division method.  The number 3 is also a non-perfect square. Hence, the value of the square root of 3 can be calculated using the long division method.

## How to find the value root of 3?

As it is mentioned above, the easiest way to finding the root value of imperfect square numbers is by using long division.

Since 3 is a non-perfect square number, we will find the value of root 3 using long division method as follows

Therefore, the value of root 3 is

√3 = 1.73205080757

While solving mathematical problems, we can use the round off value of root 3 up to three decimal place.

√3 = 1.732

### Table of Square Root

Below is the table to find the square root values from number 1 to 25.

 Number Square Root (√) 1 1.000 2 1.414 3 1.732 4 2.000 5 2.236 6 2.449 7 2.646 8 2.828 9 3.000 10 3.162 11 3.317 12 3.464 13 3.606 14 3.742 15 3.873 16 4.000 17 4.123 18 4.243 19 4.359 20 4.472 21 4.583 22 4.690 23 4.796 24 4.899 25 5.000

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## Frequently Asked Questions – FAQs

### What is the value of root 3?

The value of the square root of 3 is 1.73205080757.

### What is the approximate value of √3?

The value of √3 can be expressed up to three places of decimal as:
√3 = 1.732

### How can we find the value of √3?

To find the value of √3, we have to use long division method, because 3 is a non-perfect square number and its root does not give a natural number; instead, it is a fraction.

### What is the value of root 2 and root 5?

The value of root 2 is 1.414 and of root 5 is 2.236. It can be denoted as:
√2 = 1.414
√5 = 2.236

### What is the value of 3√4?

Since, √4 = 2, therefore,
3√4 = 3 x 2 = 6.

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