Square Root of 555

The square root is the inverse of the square of the number. 555 is not a perfect square. The square root of 555 is expressed in both radical and exponential form. In the radical form, it is expressed as √555, whereas (555)^(1/2) in exponential form. √555 ≈ 23.537, 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 useful for perfect square numbers. However, for non-perfect square numbers like 555, methods such as 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 555 is broken down into its prime factors:

Step 1: Finding the prime factors of 555 Breaking it down, we get 3 x 5 x 37: 3¹ x 5¹ x 37¹

Step 2: Since 555 is not a perfect square, the digits of the number can’t be grouped into pairs.

Therefore, calculating √555 using prime factorization directly is not possible.

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, group the numbers from right to left. In the case of 555, we group it as 55 and 5.

Step 2: Now find n whose square is ≤ 5. We can say n is '2' because 2 x 2 = 4, which is lesser than or equal to 5. The quotient is 2; after subtracting 4 from 5, the remainder is 1.

Step 3: Bring down 55 to make it the new dividend. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.

Step 4: The new divisor is 4n. We need to find the value of n such that 4n x n ≤ 155. Let n be 3, so 43 x 3 = 129.

Step 5: Subtract 129 from 155, the difference is 26, and the quotient is 23.

Step 6: Since the remainder is less than the divisor, add a decimal point. Adding the decimal point allows us to add two zeros to the dividend. Now the new dividend is 2600.

Step 7: Find the new divisor. It will be 46, as 465 x 5 = 2325.

Step 8: Subtract 2325 from 2600, we get the result 275.

Step 9: Continue doing these steps until we get two numbers after the decimal point.

So the square root of √555 is approximately 23.53.

The approximation method is another method for finding square roots. It is an easy way to find the square root of a given number. Now let us learn how to find the square root of 555 using the approximation method.

Step 1: Find the closest perfect squares to √555. The smallest perfect square less than 555 is 529, and the closest perfect square greater is 576. √555 falls between 23 and 24.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). (555 - 529) / (576 - 529) = 26 / 47 ≈ 0.553

Using the formula, we identified the decimal part of our square root. The next step is adding the initial value to the decimal number, which is 23 + 0.553 ≈ 23.553.

So the square root of 555 is approximately 23.553.

• 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, we typically use the positive square root due to its applications in the real world, 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.

• 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.