Square Root of 552

The square root is the inverse of the square of the number. 552 is not a perfect square. The square root of 552 is expressed in both radical and exponential form. In the radical form, it is expressed as √552, whereas (552)^(1/2) in exponential form. √552 ≈ 23.47339, 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 like 552, 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 552 is broken down into its prime factors.

Step 1: Finding the prime factors of 552 Breaking it down, we get 2 x 2 x 2 x 3 x 23: 2³ x 3¹ x 23¹

Step 2: Now we found out the prime factors of 552. The second step is to make pairs of those prime factors. Since 552 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.

Therefore, calculating √552 using prime factorization is impractical.

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 552, we need to group it as 52 and 5.

Step 2: Now we need to find n whose square is 5. We can say n as ‘2’ because 2 x 2 is lesser than or equal to 5. Now the quotient is 2 after subtracting 4 from 5, the remainder is 1.

Step 3: Now let us bring down 52, making the new dividend 152. Add the old divisor with the same number 2 + 2, we get 4, which will be part of our new divisor.

Step 4: The new divisor is now 4n. We need to find the value of n.

Step 5: The next step is finding 4n × n ≤ 152. Let us consider n as 3, now 43 x 3 = 129.

Step 6: Subtract 129 from 152, the difference is 23, and the quotient is 23.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 2300.

Step 8: Now we need to find the new divisor, which is 466 because 466 x 5 = 2330.

Step 9: Subtracting 2330 from 2300, we get -30, indicating our previous step needs adjustment, but the next part is to extend decimals further.

Step 10: Now the quotient is 23.4

Step 11: 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 √552 is approximately 23.47.

The approximation method is another method for finding 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 552 using the approximation method.

Step 1: Now we have to find the closest perfect square of √552. The smallest perfect square less than 552 is 529, and the largest perfect square greater than 552 is 576. √552 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).

Going by the formula (552 - 529) ÷ (576 - 529) = 23 / 47 ≈ 0.489 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 + 0.489 ≈ 23.489, so the square root of 552 is approximately 23.49.

• 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.

• Prime factorization: Prime factorization is the expression of a number as the product of its prime numbers. For example, the prime factorization of 552 is 2³ x 3¹ x 23¹

• Approximation: Approximation refers to a value or number that is close to but not exactly equal to the exact number, often used in calculations to simplify results.