Square Root of 553

The square root is the inverse of the square of a number. 553 is not a perfect square. The square root of 553 is expressed in both radical and exponential form. In the radical form, it is expressed as √553, whereas (553)^(1/2) in the exponential form. √553 ≈ 23.514, 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 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 553 is broken down into its prime factors:

Step 1: Finding the prime factors of 553 Breaking it down, we get 553 = 29 x 19

Step 2: Now we found out the prime factors of 553. The second step is to make pairs of those prime factors. Since 553 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.

Therefore, calculating 553 using prime factorization is impossible.

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 553, we need to group it as 53 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 equal to 4, which is less than 5. Now the quotient is 2, and after subtracting 4 from 5, the remainder is 1.

Step 3: Now let us bring down 53, which is the new dividend. Add the old divisor with the same number 2 + 2; we get 4, which will be our new divisor.

Step 4: The new divisor will be 4n. We need to find the value of n such that 4n x n ≤ 153. Step 5: Let us consider n as 3, now 43 x 3 = 129

Step 6: Subtract 129 from 153, the difference is 24, 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 zeroes to the dividend. Now the new dividend is 2400.

Step 8: Now we need to find the new divisor, which is 470, because 470 x 5 = 2350. Step 9: Subtracting 2350 from 2400, we get the result 50.

Step 10: Now the quotient is 23.5

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

So the square root of √553 is approximately 23.51.

The approximation method is another method for finding 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 553 using the approximation method.

Step 1: Now we have to find the closest perfect squares of √553. The smallest perfect square less than 553 is 529, and the largest perfect square greater than 553 is 576. √553 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 (553 - 529) / (576 - 529) = 24/47 = 0.51 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 + 0.51 = 23.51, so the square root of 553 is approximately 23.51.

• Square root: A square root is the inverse of squaring a number. 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 the positive square root that is commonly used due to its applications in the real world. This is why it is known as the principal square root.

• Prime number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. For example, 29 is a prime number.

• Long division method: A step-by-step process used to find the square root of non-perfect square numbers by dividing the number into smaller parts.