Square Root of 40000

The square root is the inverse of the square of the number. 40000 is a perfect square. The square root of 40000 is expressed in both radical and exponential form. In the radical form, it is expressed as √40000, whereas (40000)^(1/2) in the exponential form. √40000 = 200, 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. Since 40000 is a perfect square, we will primarily use the prime factorization method. 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 40000 is broken down into its prime factors.

Step 1: Finding the prime factors of 40000 Breaking it down, we get 2 x 2 x 2 x 2 x 5 x 5 x 5 x 5: (2^4) x (5^4)

Step 2: Now we found out the prime factors of 40000. The second step is to make pairs of those prime factors. Since 40000 is a perfect square, the digits of the number can be grouped in pairs.

Therefore, calculating √40000 using prime factorization gives us: (2^4) x (5^4) = (2 x 5)^2 = 200.

The long division method is particularly used for non-perfect square numbers, but it can also be applied to perfect squares. Here’s 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 40000, we group it as (400)(00).

Step 2: Now we need to find n whose square is less than or equal to 400. We can say n as '20' because 20 x 20 = 400.

Step 3: The quotient is 20 after subtracting 400 - 400, the remainder is 0.

Since the remainder is 0, the square root of 40000 is 200.

The approximation method is another way to find square roots. It is an easy method for estimating the square root of a given number, especially when it is not a perfect square. However, for 40000, we know the exact value, which is 200. Therefore, this method is unnecessary here.

• Square root: A square root is the inverse of a square. For example: 20^2 = 400, and the inverse of the square is the square root, which is √400 = 20.

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

• Perfect square: A perfect square is a number that is the square of an integer. For example, 40000 is a perfect square because it is the square of 200.

• Integer: Integers are the combination of whole numbers and their negatives. For example: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, etc., are integers.

• Prime factorization: Prime factorization involves breaking down a number into its prime factors. For example, the prime factorization of 40000 is 2^4 × 5^4.