Square Root of 584

The square root is the inverse of the square of the number. 584 is not a perfect square. The square root of 584 is expressed in both radical and exponential form. In the radical form, it is expressed as √584, whereas (584)^(1/2) in the exponential form. √584 ≈ 24.1661, 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: 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 584 is broken down into its prime factors: Step 1: Finding the prime factors of 584 Breaking it down, we get 2 x 2 x 2 x 73: 2^3 x 73 Step 2: Now we found out the prime factors of 584. The second step is to make pairs of those prime factors. Since 584 is not a perfect square, the digits of the number can’t be grouped in pairs. Therefore, calculating √584 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 584, we need to group it as 84 and 5. Step 2: Now we need to find n whose square is 4. We can say n is ‘2’ because 2 x 2 is lesser than or equal to 5. Now the quotient is 2, and after subtracting 4 from 5, the remainder is 1. Step 3: Now let us bring down 84, which is the new dividend. Add the old divisor with the same number 2 + 2 to get 4, which will be our new divisor. Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 4n as the new divisor, and we need to find the value of n. Step 5: The next step is finding 4n x n ≤ 184. Let us consider n as 4, now 4 x 4 = 16, and 46 x 4 = 184. Step 6: Subtract 184 from 184, and the difference is 0, and the quotient is 24. Step 7: Since there is no remainder, we can state that the square root of 584 is approximately 24.1661. For further precision, continue the long division process.

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 584 using the approximation method. Step 1: Now we have to find the closest perfect squares to √584. The smallest perfect square less than 584 is 576, and the largest perfect square greater than 584 is 625. √584 falls somewhere between 24 and 25. Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Going by the formula: (584 - 576) / (625 - 576) = 8 / 49 ≈ 0.1633 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 24 + 0.1661 ≈ 24.1661, so the square root of 584 is approximately 24.1661.

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

• Prime factorization: Prime factorization is the process of expressing a number as a product of its prime factors. For example, the prime factorization of 72 is 2 x 2 x 2 x 3 x 3.

• 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.