Square Root of 12

Square Root of 12

What is the Square root of 12? To understand Square root of 12 we need to first understand the square root of a number. The symbol for Square root is “√ “ also known as radical symbol or radix.

“The square root of a number is a value, that value when multiplied by itself gives us the desired number.”

Let’s take an example before understanding root 12, the square root of a number by breaking the definition given above. Here number will be 4 and as we need square root of 4, it can be written as √4.

Now we need a value that should multiply by itself and gives as √4

So we know when 2*2 =4

Hence our value will be 2 which multiply by itself and gives as 4.

√4 = 2

√2*2 = 2

So, when we get the value which multiplies by itself and gives us the number such numbers are called perfect square root. For example √9,√16,√25 and many more

Root 12

From the Above Information Now Let’s Find Square Root of 12

√1

1

√4

2

√9

3

√16

4


Here in the above table, we can see that √12 comes between √9 and √16 they are the perfect roots as their square root is 2 and 3 respectively.

So from this, we know that the square root of 12 will not be a perfect square.

To understand and be able to derive a square root of any number let’s first understand Prime factorization.

Value of Root 12

Finding square root through prime factorization means reducing the number to its prime numbers. So what are prime numbers? Numbers that are divisible by itself and 1 for example 2,3,5,7,11.

Root 12 Value 

To take out the root 12 value here our number will be 12 which is not a prime number because 12 has factors 1,2,3,4,6,12.

Let’s first  take an example of a perfect square root 36

√36                   

√2 x 2 x 3 x 3

√6x6

=6

From the above, we can see that the numbers which are in pairs get out from the root and which can’t that will result in a radical answer. So from this, we clearly know that root 12 is not a perfect root. 

What is the Square Root of 12?

To find out we need to first write the factors of 12 :

12= 2 x 2 x 3 Therefore the value of the square root of 12 can be written as

√12= √2 x 2 x 3 Now √22 x 3

= 2√3 ( taking the Square term out of the root) is a radical value of root 12.

When a number which can’t be simplified to remove the square root (or cube root etc) then such number is called surds. As we can see √12 = 2√3 here in our answer √3 cannot be further simplified.

Apart from the fact that √12 can also be written in decimal form by putting the value of √3 which is approximately 1.73

Therefore √12= 2 x 1.73 Which gives us 3.46 approximately. Now, this is a decimal value of root 12.

Like √12 there are many such numbers that are not a perfect square and the value can be in both radical as well decimal. 

Identify Perfect Square

Square Numbers From

1² to 10²

Square Numbers From

11² to 20²

Square Numbers From

21² to 30²

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81

10² = 100

11² = 121

12² = 144

13² = 169

14² = 196

15² = 225

16² = 256

17² = 289

18² = 324

19² = 361

20² = 400

21² = 441

22² = 484

23² = 529

24² = 576

25² = 625

26² = 676

27² = 729

28² = 784

29² = 841

30² = 900


From the above chart, if we notice the unit place of squares, they are ending with 1,4,5,6,9.

This helps us to find out that a perfect square has 1,4,5,6,9 at the unit place. As in our case square root of 12, where the unit place of 12 is 2 which is not a perfect square.

Square and Square root 

To understand the difference between the square and square root let’s take two examples:

  1. If We Say the Square of 3 is 9 (3*3)

That means if the number (here 3)  multiply by itself it gives us the square of that number.

  1. The Square Root of 9 is 3.

The square root of a number (here √9) has a value (here 3)  that multiplies by itself and gives us that number.

Fun Fact

There is an unofficial holiday known as Square Root Day and it is celebrated on days when the day and the month are the square root (√) of the last two digits of the year. 

For example, the day will be 4, the month will be April that is 4 and when day times month you will get the year that is 16 denotes 2016. 

Wait for the year 2025 when on 5th May when you will going to have a square root day on 5/5/25.

FAQ (Frequently Asked Questions)

1. Can There Be Two Square Root of a Number?

We know that 9 was the square of 3 Thus the square of -3 is also 9. All positive real numbers have two square roots. positive square root and negative square root. The positive square root is commonly referred to as the principal square root. The main reason that a number could have two square roots is that the product of two numbers is positive if both numbers have the same sign.

A square root is a radical symbol √ and the number inside the radical symbol called the radicand.

for both the positive and the negative square root of a radicand we put the symbol ± (read as plus-minus) in front of the root ±9=±3.

2.  Is √2  x √2 Equals to 2

When we Recall the meaning of a square root of a number which is a value when multiplied by itself gives us the desired number

√2  can also be written as 21/2

So when 21/2  * 21/2 

When multiplied with the same base powers will be added here in this ½ + ½  = 1

That means 2 has exponent 1 which gives as 21