Square Root of 2816

The square root is the inverse of the square of a number. 2816 is not a perfect square. The square root of 2816 is expressed in both radical and exponential form. In radical form, it is expressed as √2816, whereas in exponential form it is (2816)^(1/2). √2816 ≈ 53.057, 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, the prime factorization method is not used for non-perfect square numbers; instead, the long-division method and approximation method are used. Let us now learn the following methods:

• 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 2816 is broken down into its prime factors.

Step 1: Finding the prime factors of 2816 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 2 x 11 x 11: 2^6 x 11^2

Step 2: Now that we found the prime factors of 2816, the second step is to make pairs of those prime factors. Since 2816 is not a perfect square, the digits of the number can’t be grouped into pairs.

Thus, calculating 2816 using prime factorization is not straightforward.

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: Begin by grouping the numbers from right to left. In the case of 2816, we need to group it as 28 and 16.

Step 2: Find n whose square is less than or equal to 28. Here, n = 5 because 5 x 5 = 25. Now the quotient is 5, and after subtracting 25 from 28, the remainder is 3.

Step 3: Bring down 16, making the new dividend 316. Add the old divisor (5) with itself, giving us 10, which will be our new divisor.

Step 4: The new divisor will be 10n. We need to find n such that 10n x n ≤ 316. Let n = 3, then 103 x 3 = 309.

Step 5: Subtract 309 from 316, resulting in a remainder of 7.

Step 6: Since the dividend is less than the divisor, add a decimal point to the quotient and bring down two zeros to the remainder, making it 700.

Step 7: The new divisor will be 106. Find n such that 106n x n ≤ 700. Let n = 6, then 1066 x 6 = 636.

Step 8: Subtract 636 from 700, resulting in a remainder of 64.

Step 9: Continue doing these steps until you get two numbers after the decimal point or until the remainder is zero.

So the square root of √2816 ≈ 53.06

The approximation method is another method for finding square roots; it is an easy method to find the square root of a given number. Let us learn how to find the square root of 2816 using the approximation method.

Step 1: Find the closest perfect square of √2816. The closest perfect squares of 2816 are 2809 and 2916. √2816 falls somewhere between 53 and 54.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (2816 - 2809) / (2916 - 2809) = 7 / 107 ≈ 0.065

Step 3: Add the value obtained to the lower perfect square root: 53 + 0.065 = 53.065

So the square root of 2816 ≈ 53.065

• 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.
   
• Irrational number: An irrational number is a number that cannot be written in the form of p/q, where q is not equal to zero and p and q are integers.
   
• Perfect square: A number that is the square of an integer. For example, 9 is a perfect square because it is 3^2.
   
• Prime factorization: Breaking down a number into its basic prime number factors. For example, the prime factorization of 18 is 2 x 3 x 3.
   
• Long division method: A method used to find the square root of a number by performing division in steps to obtain a precise value.