Square Root of 144

In Mathematics, the square root of 144 is a value which when multiplied by itself gives the result 144. For example, 12 ×12= 144. Hence, we can see the square root value of 144 is 12. It is written in the radical form as 

\[\sqrt{144}=12\]. 

There are two methods to determine the square root value of 144. The two methods to determine the square root value of 144 are Prime Factorization Method and Long Division Method. In this article, we will learn both the methods that will help the students to find the square root of any numbers in a simpler and fastest way.

According to the equation given above, we can state that the square root of natural number 144 is  12. It is a value which when multiplied by itself gives the number 144.

Hence, 12 ×12  = 144.

What is the Meaning of Square Root?

The square root of any natural number is a value that is represented in the form of \[X=b\sqrt{b}\]

It implies that x is the square root of b , where b is any natural number. We can also write it as x² = b. Hence, it is concluded that the square root of any number is equal to a number which when multiplied by itself obtains back the original numbers. For Example, 5 × 5 = 25 and it can be said that the square root of a number 25 is 5.

The symbol used to represent the square root is ‘√’

The symbol of square roots is  also known as radical. The number inside the square root is known as radicand.

Square Root Methods

The two methods to find the square root of a given number are:

1. Prime Factorization Method

2. Long Division  Method

Prime Factorization Method

In the Prime factorization method, we generally determine the prime factors of a given number. The prime factorization method can easily be used as we have studied about prime factors in our previous classes. This method can only be used if the number given is a perfect square. A number calculated by squaring a number is considered as a perfect square. A perfect square is an integer whose square root is always an integer . For example, 9, 36, 144 etc are  perfect squares.

As we know,144 is a perfect square. 

Therefore, the prime factors of 144 = 2 × 2 × 2 × 2 × 3 × 3

If we take the square root of both the sides, we get

\[\sqrt{144}\] = \[\sqrt{2\times 2\times 2\times 2\times 3\times 3}\]

We can see 2 pairs of 2 and 1 pair of 3 in the above given prime factors of 144.

\[\sqrt{144}\] = 2 × 2 × 3

\[\sqrt{144}\]= 12

Hence, the square root of 144 is 12.

Method of Long Division

We may also use the long division approach to obtain the square root of any number. This procedure is quite useful and the quickest of all for locating the root. It can be used to find the root of imperfect squares and huge numbers, something that prime factorisation cannot do. The steps for using the long division approach are outlined below.

• Take the first digit, 1, and leave the remaining two digits, 4, alone.

• The square of 1 is now 1. As a result, if we use 1 as the divisor, quotient, and dividend, the residual is 0.

• We'll now deduct the other two numbers as dividends and add 1 to the divisor to get our next divisor, which is 1+1 =2.

• Because the last digit is 4, either the square of 2 or the number 8 can be used as the last digit.

• As a result, we'll add 2 to 2 and multiply by 2 to get 44, as in 22 x 2.

• As a result, the final quotient is 12, which is the answer.

The steps to find the root of 144 are listed below.