Square Root of 579

The square root is the inverse of the square of the number. 579 is not a perfect square. The square root of 579 is expressed in both radical and exponential form. In radical form, it is expressed as √579, whereas in exponential form it is expressed as (579)^(1/2). √579 ≈ 24.0624, 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 and approximation methods are used. 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 579 is broken down into its prime factors:

Step 1: Finding the prime factors of 579 Breaking it down, we get 3 x 193: 3^1 x 193^1

Step 2: Now we have found the prime factors of 579. Since 579 is not a perfect square, the digits of the number can’t be grouped into pairs.

Therefore, calculating √579 using prime factorization is not feasible.

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 579, we need to group it as 79 and 5.

Step 2: Now we need to find a number whose square is close to 5. We can choose 2 because 2 x 2 = 4, which is less than 5. The quotient is 2, and after subtracting 4 from 5, the remainder is 1.

Step 3: Now let us bring down 79, which is the new dividend. Add the old divisor with the same number, 2 + 2 = 4, which will be our new divisor.

Step 4: We need to find a digit x such that 4x x x is less than or equal to 179. Choosing x as 4, we get 44 x 4 = 176.

Step 5: Subtract 176 from 179, the difference is 3, and the quotient is 24.

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 300.

Step 7: Find the new divisor that is 48 because 48 x 6 = 288, which is less than 300. Step 8: Subtracting 288 from 300, we get 12. Step 9: Continue these steps until we get two numbers after the decimal point.

So the square root of √579 ≈ 24.06

The approximation method is another method for finding square roots, an easy method to find the square root of a given number. Now let us learn how to find the square root of 579 using the approximation method.

Step 1: Now we have to find the closest perfect squares of √579. The smallest perfect square less than 579 is 529 (23 x 23) and the largest perfect square greater than 579 is 625 (25 x 25). √579 falls somewhere between 23 and 25.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) ÷ (Largest perfect square - smallest perfect square) Using the formula, (579 - 529) ÷ (625 - 529) ≈ 0.5263 Add this decimal to the smaller whole number: 23 + 0.5263 ≈ 23.53, so the square root of 579 is approximately 23.53.

• 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. This is why it is also known as the principal square root.

• Prime factorization: It is the process of expressing a number as the product of its prime factors.

• Perfect square: A number that is the square of an integer. For example, 16 is a perfect square because it is 4^2.