Square Root of 6724

The square root is the inverse of the square of the number. 6724 is a perfect square. The square root of 6724 is expressed in both radical and exponential form. In the radical form, it is expressed as √6724, whereas (6724)^(1/2) in the exponential form. √6724 = 82, which is a rational number because it can 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 long division method and approximation method can also be used for non-perfect square numbers. 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 6724 is broken down into its prime factors. Step 1: Finding the prime factors of 6724 Breaking it down, we get 2 × 2 × 41 × 41: 2^2 × 41^2 Step 2: Now we found out the prime factors of 6724. The second step is to make pairs of those prime factors. Since 6724 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating the square root of 6724 using prime factorization is possible.

The long division method is particularly used for both perfect and non-perfect square numbers. 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 6724, we need to group it as 67 and 24. Step 2: Now we need to find n whose square is closest to 67. We can say n is ‘8’ because 8 × 8 = 64, which is lesser than or equal to 67. Now the quotient is 8 after subtracting 67 - 64, the remainder is 3. Step 3: Now let us bring down 24, which is the new dividend. Add the old divisor (8) with the same number (8), we get 16, which will be our new divisor. Step 4: The new divisor is now 16, and we need to find the value of n such that 16n × n ≤ 324. Step 5: The next step is finding n. If n is 2, then 16 × 2 × 2 = 324. Step 6: Subtract 324 from 324. The remainder is 0, and the quotient is 82. Since the remainder is zero, the square root of 6724 is 82.

The approximation method is another method for finding the square roots, and 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 6724 using the approximation method. Step 1: Now we have to find the closest perfect square of √6724. Since 6724 is a perfect square itself, we know that √6724 = 82. Step 2: Alternatively, you can check that 6724 is between perfect squares of 81^2 = 6561 and 83^2 = 6889. Since 6724 is closer to 6889, we validate that 82 is indeed the correct square root.

Square root: A square root is the inverse of the square. Example: 9^2 = 81, and the inverse of the square is the square root that is √81 = 9. Rational number: A rational number is a number that can be written in the form of p/q, q is not equal to zero, and p and q are integers. Perfect square: A perfect square is a number that can be expressed as the square of an integer. For example, 81 is a perfect square because it is 9^2. Prime factorization: Prime factorization is the process of expressing a number as the product of its prime factors. Long division method: A method used to find the square roots of numbers, both perfect and non-perfect squares, by breaking down the number through division steps.