Square Root of 8100

The square root is the inverse of the square of the number. 8100 is a perfect square. The square root of 8100 is expressed in both radical and exponential form. In the radical form, it is expressed as √8100, whereas (8100)^(1/2) in exponential form. √8100 = 90, 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. Since 8100 is a perfect square, the prime factorization method is appropriate. We can also use the long division method and approximation method if needed. 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 8100 is broken down into its prime factors:

Step 1: Finding the prime factors of 8100 Breaking it down, we get 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5: (2^2) × (3^4) × (5^2)

Step 2: Now we found out the prime factors of 8100. The next step is to make pairs of those prime factors. (2^2) = 2, (3^4) = 3 × 3 = 9, (5^2) = 5

Step 3: Multiplying the results, we get 2 × 9 × 5 = 90 Therefore, the square root of 8100 is 90.

The long division method is particularly useful for large numbers. 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 pairs. In the case of 8100, we group it as 81 and 00.

Step 2: Now we need to find n whose square is 81. We can say n as '9' because 9 × 9 is equal to 81. Now the quotient is 9, and after subtracting 81-81, the remainder is 0.

Step 3: Now let us bring down 00, which is the new dividend. The divisor becomes 90.

Step 4: The new divisor will be 90, and since the remainder is 0, we conclude that the square root of 8100 is 90.

Approximation method is another method for finding square roots, but since 8100 is a perfect square, the approximation method confirms the calculation.

Step 1: Identify the closest perfect squares, √8100 is between √6400 (80) and √10000 (100).

Step 2: Since 8100 is a perfect square, we don't need further approximation as the exact square root is already determined to be 90.

• Square root: A square root is the inverse of a square. Example: 10^2 = 100, and the inverse of the square is the square root, that is, √100 = 10.
   
• 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, 8100 is a perfect square because it is 90^2.
   
• Integers: The combination of whole numbers and negative numbers are integers. For example: -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7… are integers.
   
• Exponential form: A way of expressing numbers involving powers or exponents. For example, 8100^(1/2) is the exponential form of √8100.