Square root of 10 

The square of a number denotes the value when a number is multiplied by itself. Square root means to find the root number, which makes the given number a perfect square. It is denoted by the symbol √ known as radical or radix. For example, the square root of 10 is irrational, with never-ending digits after the decimal. A square root will always have a positive and a negative value.

Square root of 10 is ±3.16227…

We need to check the unit place of a number to find the perfect square.

1. If the number ends with 2, 3, 7 and 8, then the number may not be a perfect square.
2. If the number ends with 1, 4, 5, 6, and 9, there’s a possibility that the number may be a perfect square.

Square root of 10

Since 10 is not a perfect square, as it ends with number 0, we need to find the square root of 10 using different methods – long division and finding square root using unit places.

1. Using unit places
   
   We know, number 10 is not a prime number. A prime number is the one which is divisible by 1 and the number itself. But number 10 can be factored into 2 and 5. Hence, number 10 is not a prime number.
   
   We can write, 10 = 2 x 5
   
   Also, putting radical symbol on both side, we get √10 = √(2×5) = √ 2× √5
   
   √10 = 1.414 x 2.236 = ±3.162 approximately.


2. By long division method
    
   1. Make pairs of the numbers after the decimal places.
   2. Choose such a number that is a perfect square and is less than 10. In this case, it will be number 3 because the square of number 3 is 9, which is less than 10.
   3. Write 3 at the place of divisor and quotient. Subtract 9 from 10. We will get remainder 1.
   4. Add the divisor, making it to 6. Write down another pair of numbers like we do in the normal division method.
   5. Now, we need to find a number whose square is less than 100. In this case it will be 61.
   6. Write 1 on the place of divisor and quotient. We will get the remainder as 39.
   7. Perform the same steps to find the square root up to 3-4 decimal places.
   8. This is the long method to find the square root of 10. One can find square roots of 100, 1000 and so on with the same method.

Square root values to memorise

Do you know?

1. Ancient Indians have been using square roots since 800 BCE.
2. Mahavira, an ancient Indian mathematician, was the first one to announce the negative value of a square root.
3. The procedure to find out the square root of a number was written in the book Writings and Reckonings during the Han dynasty around 200 BCE.