Square Root of 16200

The square root is the inverse of the square of the number. 16200 is not a perfect square. The square root of 16200 is expressed in both radical and exponential form. In radical form, it is expressed as √16200, whereas in exponential form it is (16200)^(1/2). √16200 ≈ 127.2792, which is an irrational number because it cannot 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:

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 us look at how 16200 is broken down into its prime factors.

Step 1: Finding the prime factors of 16200 Breaking it down, we get 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 5: 2³ x 3⁴ x 5²

Step 2: Now we found out the prime factors of 16200. The second step is to make pairs of those prime factors. Since 16200 is not a perfect square, therefore the digits of the number can’t be grouped in pairs completely.

Therefore, calculating 16200 using prime factorization gives us an approximate value.

The long division method is particularly used for 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 16200, we group it as 16 and 200.

Step 2: Find n whose square is less than or equal to 16. We can say n is ‘4’ because 4 x 4 = 16. The quotient is 4, and after subtracting 16 - 16, the remainder is 0.

Step 3: Bring down 200, which is the new dividend. Add the old divisor with the same number 4 + 4 = 8, which will be our new divisor.

Step 4: The new divisor becomes 8n. We need to find the value of n where 8n x n ≤ 200.

Step 5: Consider n as 2, now 8 x 2 x 2 = 32. Subtract 32 from 200, the difference is 168, and the quotient becomes 42.

Step 6: Since the dividend is less than the divisor, add a decimal point and zeros to the dividend. Now the new dividend is 16800.

Step 7: Find the new divisor. Use the new divisor and repeat the process until the required precision is achieved.

So the square root of √16200 is approximately 127.28.

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 16200 using the approximation method.

Step 1: Find the closest perfect square to √16200. The smallest perfect square near 16200 is 14400, and the largest is 16900. √16200 falls between 120 and 130.

Step 2: Apply the formula (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).

Using the formula (16200 - 14400) ÷ (16900 - 14400) ≈ 0.72. Using the formula, we identified the decimal point of our square root. The next step is adding this value to the initial approximation, which is 120 + 7.28 ≈ 127.28.

• Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, that is, √16 = 4.

• Irrational number: An irrational number cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.

• Principal square root: A number has both positive and negative square roots; however, it is always the positive square root that is more prominent due to its uses in the real world. This is why it is known as the principal square root.

• Prime factorization: The process of breaking down a number into its prime factors. Example: The prime factorization of 16200 is 2³ x 3⁴ x 5².

• Approximation method: A technique used to find an approximate value of a number, especially useful for non-perfect squares.