Square root of 144

The square root of 144 is ±12.The positive value, 12 is the solution of the equation x² = 144. As defined, the square root is just the inverse of squaring a number, so, squaring 12 will result in 144.  The square root of 144 is expressed as √144 in radical form, where the ‘√’  sign is called “radical”  sign. In exponential form, it is written as (144)^1/2  
 

We can find the square root of 144 through various methods. They are:

• Prime factorization method

• Long division method

• Approximation/Estimation method
   

The prime factorization of 144 involves breaking down a number into its factors. Divide 144 by prime numbers, and continue to divide the quotients until they can’t be separated anymore. After factorizing 144, make pairs out of the factors to get the square root. If there exists numbers which cannot be made pairs further, we place those numbers with a “radical” sign along with the obtained pairs

So, Prime factorization of 144 = 2 × 2  × 2 × 2 × 3 × 3   

for 144, two pairs of factor 2 and one pair of factors 3 can be obtained.

So, it can be expressed as  √144 = √(2 × 2  × 2 × 2 × 3 × 3) = 2 × 2 × 3 = 12

12 is the simplest radical form of √144

This is a method used for obtaining the square root for non-perfect squares, mainly. It usually involves the division of the dividend by the divisor, getting a quotient and a remainder too sometimes.

Follow the steps to calculate the square root of 144:

Step 1: Write the number 144 and draw a bar above the pair of digits from right to left.

Step 2: Now, find the greatest number whose square is less than or equal to 1. Here, it is1 because 1²=1

Step 3: now divide 1 by 1 (the number we got from Step 2) such that we get 1 as a quotient, and we get a remainder.  Double the divisor 1, we get 2, and then the largest possible number A1=2 is chosen such that when 2 is written beside the new divisor 2, a 2-digit number is formed →22, and multiplying 2 with 22 gives 44, which is equal to 0 on subtracting from 44.

Repeat this process until you reach the remainder of 0. 

Step 4: The quotient obtained is the square root of 144. In this case, it is 12.

roots through the repeated subtraction method. Furthermore, we just have to subtract consecutive odd numbers from the given number, starting from 1. The square root of the given number will be the count of the number of steps required to obtain 0. Here are the steps:

Step 1: take the number 144 and then subtract the first odd number from it. Here, in this case, it is 144-1=143

Step 2: we have to subtract the next odd number from the obtained number until it comes zero as a result. Now take the obtained number (from Step 1), i.e., 143, and again subtract the next odd number after 1, which is 3, → 143-3=140. Like this, we have to proceed further.

Step 3: now we have to count the number of subtraction steps it takes to yield 0 finally. 

Here, in this case, it takes 12 steps 

So, the square root is equal to the count, i.e., the square root of 144 is ±12.

• Exponential form:  An algebraic expression that includes an exponent. It is a way of expressing the numbers raised to some power of their factors. It includes continuous multiplication involving base and exponent. Ex: 2 × 2 × 2 × 2 = 16 Or, 2⁴ = 16, where 2 is the base, 4 is the exponent 

• Prime Factorization:  Expressing the given expression as a product of its factors. Ex: 48=2 × 2 × 2 × 2 × 3

• Prime Numbers: Numbers which are greater than 1, having only 2 factors as →1 and Itself. Ex: 1,3,5,7,....

• Rational numbers and Irrational numbers: The Number which can be expressed as p/q, where p and q are integers and q not equal to 0 are called Rational numbers. Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. 

• Perfect and non-perfect square numbers: Perfect square numbers are those numbers whose square roots do not include decimal places. Ex: 4,9,25 Non-perfect square numbers are those numbers whose square roots comprise decimal places. Ex :3, 8, 24