# Square Root of 10

The square number or square of a number is obtained when we multiply that number by that number itself. But there are different methods and representations available to find 10 . square root of Consider some examples for square numbers.

for example,

4 = 4 × 4 = 16, which is a number 4. denotes the class of

11 = 11 × 11 = 121, which is a number 11. denotes the class of

8 = 8 × 8 = 64, which is a number 8. denotes the class of

So, in the above examples, 4, 10 and 8 are square numbers. If we want to find out whether a given number is a perfect square or not, then check the unit place of a number.

• If the number ends with 2,3,7 and 8 then the number is not a perfect square.
• If the unit place of a number ends in 1,4,5,6 and 9 then that number is called a perfect square.

## How to find the square root of 10?

Finding the square root of 10 is a bit complicated because the number…… because the number 10 is not a perfect square with the number 0 in its unit place. Finding the square root of a number is the opposite process of finding the square root of a number. We can find the square root of 10 using two methods. One method is to find the original value using unit places and the other method is with the help of long division method. From the above examples, we can see that the numbers 16, 121 and 64 are perfect squares, whose unit places are 6, 1 and 4 respectively.

The symbol representing the square root is ‘ ‘ . This  is also called Radix or Radix. The number below the square root sign is called the radix. The value of square root is represented in radix as well as in decimal form. Here we will discuss the square root of 10, where the number 10 is called the radix.

#### What is the square root of 10?

The radix of 10 or the square root of 10 is represented as 10 . We know that the number 10 is an even number but it is not a prime number. Prime numbers have the property of having only two factors of a number such as 1 and the number itself. But as we know, there are four factors of 10, 1,2,5 and 10 itself, it is not a prime number and the factors are written as

1 × 10 = 10

2 × 5 = 10

5 × 2 = 10

10 × 1 = 10

But when the question comes, how can we find the square roots for the value of 10? First, write the factors of 10 as given below.

10 = 2 × 5

In the above expression, you can see that the square number is not available on the right side. So, the square root of 10 can be written as;

\sqrt{10} = \sqrt{2 × 5}

We cannot remove the square term from the root, because it has no square term and is written as,

\sqrt{10} = \sqrt{2}\sqrt{5}

The original form of the above expression is \square{10}, If we want to write it in decimal form, then enter the value of \sqrt{2}and \class{5}Which is roughly equal to 1.414 and 2.236 respectively. Hence,\class{10} = 1.414 × 2.236

\class{10}= ±3.162 approx.

#### square root of 10 by long division method

Long division method is used to find the square root of approximately 10. Use the long division process to find the value as follows.

Similarly, for numbers like 10 that are not perfect squares, use the same method to find the square root value. For example, 12, 18, 20, 27, etc. are not perfect squares, as they give the square root value in radix as well as in decimal form.