Square Root of 43560

The square root is the inverse of the square of the number. 43560 is a perfect square. The square root of 43560 is expressed in both radical and exponential form. In the radical form, it is expressed as √43560, whereas (43560)^(1/2) in the exponential form. √43560 = 208, 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, for non-perfect square numbers, 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 43560 is broken down into its prime factors:

Step 1: Finding the prime factors of 43560 Breaking it down, we get 2 x 2 x 2 x 3 x 5 x 11 x 11: 2^3 x 3 x 5 x 11^2

Step 2: Now we found out the prime factors of 43560. The second step is to make pairs of those prime factors. Since 43560 is a perfect square, the prime factors can be grouped into pairs.

Therefore, calculating √43560 using prime factorization is possible. √43560 = √(2^2 x 3 x 5 x 11^2) = 2 x 11 x 5 = 208

The long division method is particularly used for finding square roots of numbers, perfect or not. 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 pair the digits of the number from right to left. In the case of 43560, we need to group it as 43 and 560.

Step 2: Now we need to find a number whose square is less than or equal to 43. In this case, 6^2 = 36 is less than 43. So, the quotient is 6, and after subtracting 36 from 43, the remainder is 7.

Step 3: Bring down the next pair 560 to make it 7560.

Step 4: Double the quotient (6) and write it as 12, then find a digit n such that 12n x n is less than or equal to 7560.

Step 5: By trial, n is found to be 8, making 128 x 8 = 1024. Subtract 1024 from 7560 to get the remainder 0.

So the square root of √43560 is 208.

Approximation method is another method for finding the 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 43560 using the approximation method.

Step 1: Now we have to find the perfect squares closest to √43560. The exact perfect square for 43560 is 208 x 208.

So, √43560 is exactly 208.

• 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.

• Rational number: A rational number is a number that can be written in the form of p/q, where q is not zero, and p and q are integers.

• Perfect square: A number that is the square of an integer. Example: 43560 is a perfect square because 208 x 208 = 43560.

• Prime factorization: Expressing a number as the product of its prime factors.

• Perimeter: The continuous line forming the boundary of a closed geometrical figure, such as a rectangle. In this context, the perimeter of a rectangle = 2 × (length + width).