Square Root of 544

The square root is the inverse of the square of the number. 544 is not a perfect square. The square root of 544 is expressed in both radical and exponential form. In the radical form, it is expressed as √544, whereas in the exponential form it is expressed as (544)^(1/2). √544 ≈ 23.3238, 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, the prime factorization method is not used for non-perfect square numbers where the long-division method and approximation method are used. Let us now learn the following methods: -

1. Prime factorization method 
2. Long division method 
3. Approximation method

The product of prime factors is the prime factorization of a number. Now let us look at how 544 is broken down into its prime factors:

Step 1: Finding the prime factors of 544 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 17: 2^5 x 17

Step 2: Now we found out the prime factors of 544. The second step is to make pairs of those prime factors. Since 544 is not a perfect square, the digits of the number can’t all be grouped into pairs.

Therefore, calculating √544 using prime factorization will not give an exact whole number.

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 544, we need to group it as 44 and 5.

Step 2: Now we need to find n whose square is 5. We can say n is ‘2’ because 2² is less than or equal to 5. Now the quotient is 2; subtracting 2² from 5 gives a remainder of 1.

Step 3: Bring down 44, making the new dividend 144. Add the old divisor with the quotient: 2 + 2 = 4, which will be our new divisor.

Step 4: With the new divisor formed, we need to find the value of n for 4n × n ≤ 144. Let us consider n as 3, so 43 x 3 = 129.

Step 5: Subtract 129 from 144; the difference is 15. The quotient is now 23.

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 1500.

Step 7: The new divisor becomes 466 because 466 x 3 = 1398.

Step 8: Subtract 1398 from 1500, which results in 102. Step 9: The quotient is now 23.3.

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

So, the square root of √544 is approximately 23.32.

The approximation method is another way to find the square roots; 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 544 using the approximation method.

Step 1: Now we have to find the closest perfect squares of √544. The smallest perfect square less than 544 is 529, and the largest perfect square greater than 544 is 576. √544 falls somewhere between 23 and 24.

Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square).

Using the formula: (544 - 529) ÷ (576 - 529) = 15 ÷ 47 ≈ 0.319 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 23 + 0.319 ≈ 23.32. Thus, the square root of 544 is approximately 23.32.

• Square root: A square root is the inverse operation of squaring a number. Example: 4² = 16, and the inverse of the square is the square root; thus, √16 = 4.

• Irrational number: An irrational number is a number that cannot be expressed as a simple fraction (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, the positive square root is used more often in real-world applications. This is known as the principal square root.

• Perfect square: A perfect square is a number that is the square of an integer. For example, 16 is a perfect square because it is 4².

• Long division method: A step-by-step approach used to find the square root of a non-perfect square number by dividing and averaging.