Square Root of 1900

The square root is the inverse of the square of the number. 1900 is not a perfect square. The square root of 1900 is expressed in both radical and exponential form. In the radical form, it is expressed as √1900, whereas (1900)^(1/2) in the exponential form. √1900 ≈ 43.58899, 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 prime factorization method is not used; instead, the long division method and the 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 1900 is broken down into its prime factors.

Step 1: Finding the prime factors of 1900. Breaking it down, we get 2 x 2 x 5 x 5 x 19: 2^2 x 5^2 x 19

Step 2: Now we have found the prime factors of 1900. The second step is to make pairs of those prime factors. Since 1900 is not a perfect square, the digits of the number can’t be grouped in pairs without a remainder.

Therefore, calculating 1900 using prime factorization to find an exact square root 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 1900, we need to group it as 00 and 19.

Step 2: Now we need to find a number whose square is less than or equal to the first group, 19. We can say n as ‘4’ because 4 x 4 = 16, which is less than 19. Now the quotient is 4; after subtracting 16 from 19, the remainder is 3.

Step 3: Now let us bring down 00, making the new dividend 300. 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 8n, where n is added to the quotient. We need to find the value of n such that 8n x n ≤ 300. Let n be 3 because 83 x 3 = 249.

Step 5: Subtract 249 from 300; the difference is 51.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to bring down two zeroes to the dividend, making it 5100.

Step 7: Now we need to find a new divisor and continue this process until we have an adequate number of decimal places or a remainder of zero. So the square root of √1900 ≈ 43.58899.

The approximation method is another way to find 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 1900 using the approximation method.

Step 1: Find the closest perfect squares around √1900. The smallest perfect square less than 1900 is 1849 (43^2), and the largest perfect square greater than 1900 is 1936 (44^2). √1900 falls somewhere between 43 and 44.

Step 2: Now apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula: (1900 - 1849) / (1936 - 1849) = 51 / 87 ≈ 0.586

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: 43 + 0.586 ≈ 43.586.

So the square root of 1900 is approximately 43.586.

• Square root: A square root is the inverse operation of squaring a number. Example: 4^2 = 16, and the inverse is √16 = 4.

• Irrational number: An irrational number cannot be written as a simple fraction or ratio. Its decimal form is non-repeating and non-terminating.

• Perfect square: A number that is the square of an integer. For example, 9 is a perfect square because it is 3^2.

• Long division method: A technique used to find the square root of non-perfect square numbers by dividing them into smaller parts and approximating the value.

• Decimal approximation: The process of finding a non-integer value that is close enough to the exact value, often used for irrational numbers.