Square Root of 16900

The square root is the inverse of the square of the number. 16900 is a perfect square. The square root of 16900 is expressed in both radical and exponential form. In the radical form, it is expressed as √16900, whereas (16900)^(1/2) in the exponential form. √16900 = 130, 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. The long division method and approximation method can also be used for both perfect and non-perfect squares. Let's explore these methods:

1. Prime factorization method
2. Long division method
3. Approximation method

The product of prime factors is the prime factorization of a number. Now let's see how 16900 is broken down into its prime factors.

Step 1: Finding the prime factors of 16900 Breaking it down, we get 2 x 2 x 5 x 5 x 13 x 13: 2² x 5² x 13²

Step 2: Now that we have found the prime factors of 16900, the next step is to make pairs of those prime factors. Since 16900 is a perfect square, the digits of the number can be grouped into pairs.

Therefore, calculating √16900 using prime factorization is possible, resulting in 130.

The long division method is used for both perfect and non-perfect square numbers. Let's 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 16900, we need to group it as 169 and 00.

Step 2: Now we need to find n whose square is 169. We can say n is ‘13’ because 13 x 13 = 169. The quotient is 13, and after subtracting 169 from 169, the remainder is 0.

Step 3: Since the remainder is zero, no further steps are needed. The square root of 16900 is 130.

The approximation method is another way to find square roots; it is an easy method to find the square root of a given number. However, since 16900 is a perfect square, we can directly use its exact value, which is 130.

• Square root: A square root is the inverse of a square. Example: 130² = 16900, and the inverse of the square is the square root that is √16900 = 130.

• 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 an integer that is the square of an integer. Example: 16900 is a perfect square because it is 130².

• Prime factorization: The process of expressing a number as a product of its prime factors. Example: The prime factorization of 16900 is 2² x 5² x 13².

• Integer: Integers include all whole numbers and their negatives. Example: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 are integers.