Square Root Of 12

We get square of a number when we multiply the number to itself. But finding the square root of 12 consist of different methods and representation. Let us first take the examples of a few squares.

For example,

112 represents the square of 11 which is equal to 11 × 11 = 121

92 represents the square of 9 which is equal to 9 × 9 = 81

52 represents the square of 5 which is equal to 5 × 5 = 25

Therefore, in the above examples, 11, 9 and 5 are the square numbers. But if we have to find out, if a number is a perfect square or not, we need to check the unit place of the number.

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

So, we can say to find the square root of 12 is a little complicated one to solve because 12 is not a perfect square which has number 2 at its unit place. But, from the above examples, we can see number 121, 81 and 25 are the perfect squares, which have the unit place as 1, 1 and 5 respectively.

The square root is represented by the symbol, ‘√’. This symbol ‘√’ is called a radical symbol or radix. The number underneath the radical symbol or radix is called as radicand. Apart from representing the square root of 12 in radical form, it could be represented as in decimal form. Here we will find out the square root of 12, where 12 is the radicand.

What is the square root of 12?

The square root of 12 is represented in the form of \(\sqrt{12}\). Number 12 is an even number and not a prime number. Prime numbers have only two factors, 1 and the number itself, such as 1, 3, 5, etc. But as we know, 12 have six multiple factors, 1,2,3,4,6 and 12 itself, such as,

1 × 12 = 12

2 × 6 = 12

3 × 4 = 12

4 × 3 = 12

6 × 2 = 12

12 × 1 = 12

But the question comes, how can we find out the square root value of 12? First, let us write the factors of 12 as given below.

12 = 2 × 2 × 3

You can see, in the above expression, there is only one square number available on the right-hand side. Therefore, the square root of 12 can be written as;

\(\sqrt{12} = \sqrt{2 × 2 × 3}\)

Taking out the square term out of the root we get,

\(\sqrt{12} = 2 \sqrt{3}\)

This is the radical form of \(\sqrt{12}\). We can also write it in decimal form, by putting the value of \(\sqrt{3}\) which is approximately 1.73. Hence,

\(\sqrt{12}\) = 2 × 1.73

\(\sqrt{12}\) = ±3.46 approximately.

Like 12, there are also many numbers which are not perfect squares. For example, 18, 20, 27, etc. are not perfect squares, as they give the value in radical form or in decimal form.

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