Square Root of 244

The square root is the inverse of the square of the number. 244 is not a perfect square. The square root of 244 is expressed in both radical and exponential form. In the radical form, it is expressed as √244, whereas (244)^(1/2) in the exponential form. √244 ≈ 15.6205, which is an irrational number because it cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0.

The prime factorization method is used for perfect square numbers. However, for non-perfect square numbers, the prime factorization method is not used. Instead, the long-division and approximation methods are applied. Let us now learn the following methods:

• Prime factorization method
• Long division method
• Approximation method

The product of prime factors is the prime factorization of a number. Now let us look at how 244 is broken down into its prime factors.

Step 1: Finding the prime factors of 244 Breaking it down, we get 2 x 2 x 61: 2^2 x 61

Step 2: Now we found out the prime factors of 244. The second step is to make pairs of those prime factors. Since 244 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √244 using prime factorization is not straightforward.

The long division method is particularly used for non-perfect square numbers. In this method, we should check the closest perfect square number for the given number. Let us now learn how to find the square root using the long division method, step by step.

Step 1: To begin with, we need to group the numbers from right to left. In the case of 244, we need to group it as 44 and 2.

Step 2: Now we need to find n whose square is closest to 2. We can say n as ‘1’ because 1 x 1 is lesser than or equal to 2. Now the quotient is 1, and after subtracting 1 from 2, the remainder is 1.

Step 3: Now let us bring down 44, which is the new dividend. Add the old divisor with the same number 1 + 1 to get 2, which will be our new divisor.

Step 4: The new divisor will be 2n. We need to find the value of n such that 2n x n is closest to 144. Let us consider n as 5, now 25 x 5 = 125.

Step 5: Subtract 125 from 144, the difference is 19, and the quotient is 15.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 1900.

Step 7: Now we need to find a new divisor. Let us find the value of n such that 310n x n is closest to 1900. We find that n is 6 because 316 x 6 = 1896.

Step 8: Subtracting 1896 from 1900, we get the result 4.

Step 9: Now the quotient is 15.6

Step 10: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue until the remainder is zero.

So the square root of √244 is approximately 15.62.

The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. Now let us learn how to find the square root of 244 using the approximation method.

Step 1: Now we have to find the closest perfect squares of √244. The smallest perfect square less than 244 is 225, and the largest perfect square greater than 244 is 256. √244 falls somewhere between 15 and 16.

Step 2: Now we need to apply the formula (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Using the formula (244 - 225) ÷ (256 - 225) = 19 ÷ 31 = 0.6129 Using the formula, we identified the decimal point of our square root. The next step is adding the value we got initially to the decimal number, which is 15 + 0.6129 ≈ 15.62, so the square root of 244 is approximately 15.62.

• Square root: A square root is the inverse of a square. Example: 4^2 = 16, and the inverse of the square is the square root, that is √16 = 4.
   
• Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero, and p and q are integers.
   
• Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.
   
• Perfect square: A number that can be expressed as the product of an integer with itself. For example, 16 is a perfect square because it is 4 x 4.
   
• Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.