Square Root of 1881

The square root is the inverse of the square of the number. 1881 is not a perfect square. The square root of 1881 is expressed in both radical and exponential form. In the radical form, it is expressed as √1881, whereas (1881)^(1/2) in the exponential form. √1881 ≈ 43.386, 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 where long-division method and approximation method are used. 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 1881 is broken down into its prime factors.

Step 1: Finding the prime factors of 1881 Breaking it down, we get 3 x 3 x 11 x 19: 3^2 x 11 x 19

Step 2: Now we found out the prime factors of 1881. The second step is to make pairs of those prime factors. Since 1881 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.

Therefore, calculating 1881 using prime factorization is impossible.

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 1881, we need to group it as 81 and 18.

Step 2: Now we need to find n whose square is 18. We can say n as ‘4’ because 4 x 4 is lesser than or equal to 18. Now the quotient is 4, and after subtracting 16 from 18, the remainder is 2.

Step 3: Now let us bring down 81, which is the new dividend. Add the old divisor with the same number 4 + 4 to get 8, which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 8n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 8n x n ≤ 281. Let us consider n as 3, now 8x3x3 = 243.

Step 6: Subtract 243 from 281, the difference is 38, and the quotient is 43.

Step 7: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 3800.

Step 8: Now we need to find the new divisor that is 433 because 433 x 8 = 3464.

Step 9: Subtracting 3464 from 3800 we get the result 336.

Step 10: Now the quotient is 43.3.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there is no decimal values continue till the remainder is zero.

So the square root of √1881 is approximately 43.39

Approximation method is another method for finding the 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 1881 using the approximation method.

Step 1: Now we have to find the closest perfect square of √1881. The smallest perfect square less than 1881 is 1764 (42^2) and the largest perfect square greater than 1881 is 1936 (44^2). √1881 falls somewhere between 42 and 44.

Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square).

Going by the formula (1881 - 1764) ÷ (1936 - 1764) = 117 ÷ 172 = 0.68.

Using the formula, we identified the decimal point of our square root.

The next step is adding the value we got initially to the decimal number which is 42 + 0.68 = 42.68.

However, since we know 1881 is closer to 44, we can adjust the approximation to around 43.39.

• 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.

• Principal square root: A number has both positive and negative square roots, but the positive square root is often used because of its applications in the real world. This is known as the principal square root.

• Prime factorization: It is the process of expressing a number as the product of its prime factors.

• Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example, 7.86, 8.65, and 9.42 are decimals.