Square Root of 4356

The square root is the inverse of the square of the number. 4356 is a perfect square. The square root of 4356 is expressed in both radical and exponential form. In the radical form, it is expressed as √4356, whereas (4356)^(1/2) in the exponential form. √4356 = 66, 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 can be used for perfect square numbers. For non-perfect square numbers, methods like the 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 4356 is broken down into its prime factors.

Step 1: Finding the prime factors of 4356

Breaking it down, we get 2 x 2 x 3 x 3 x 11 x 11: 2^2 x 3^2 x 11^2

Step 2: Now we found out the prime factors of 4356. The second step is to make pairs of those prime factors. Since 4356 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating √4356 using prime factorization is possible.

The long division method is particularly used for both perfect and 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 4356, we need to group it as 56 and 43.

Step 2: Now we need to find n whose square is ≤ 43. We can say n is ‘6’ because 6 x 6 = 36, which is less than 43. Now the quotient is 6, and after subtracting 36 from 43, the remainder is 7.

Step 3: Now let us bring down 56, which is the new dividend. Add the old divisor with the same number, 6 + 6, we get 12, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 12n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 12n x n ≤ 756. Let us consider n as 6, now 12 x 6 x 6 = 756.

Step 6: Subtract 756 from 756, the difference is 0, and the quotient is 66.

Step 7: Since the remainder is zero, we have completely determined the square root.

So the square root of √4356 is 66.

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 4356 using the approximation method.

Step 1: Now we have to find the closest perfect square of √4356. The closest perfect square to 4356 is itself, as 66 x 66 = 4356. Using this method, we conclude that the square root of 4356 is exactly 66.

• Square root: A square root is the inverse of a square. Example: 8^2 = 64 and the inverse of the square is the square root, that is, √64 = 8.

• Perfect square: A number that has an integer as its square root. Example: 64 is a perfect square because √64 = 8.

• Rational number: A rational number is a number that can be expressed as the quotient of two integers, p/q, where q is not equal to zero.

• Long division method: A method used to calculate the square root of a number using a step-by-step division process.

• Prime factorization: Expressing a number as the product of its prime numbers. For example, the prime factorization of 4356 is 2^2 x 3^2 x 11^2.