Square Root of 1950

The square root is the inverse of the square of the number. 1950 is not a perfect square. The square root of 1950 is expressed in both radical and exponential form. In the radical form, it is expressed as √1950, whereas (1950)^(1/2) in the exponential form. √1950 ≈ 44.1588, 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 1950 is broken down into its prime factors.

Step 1: Finding the prime factors of 1950. Breaking it down, we get 2 x 3 x 3 x 5 x 13: 2^1 x 3^2 x 5^1 x 13^1

Step 2: Now we found out the prime factors of 1950. The second step is to make pairs of those prime factors. Since 1950 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.

Therefore, calculating 1950 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: To begin with, we need to group the numbers from right to left. In the case of 1950, we need to group it as 50 and 19.

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

Step 3: Now let us bring down 50, 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 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 ≤ 350. Let us consider n as 4, now 84 x 4 = 336.

Step 6: Subtract 336 from 350; the difference is 14, and the quotient is 44.

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 1400.

Step 8: Now we need to find the new divisor that is 881 because 881 x 1 = 881.

Step 9: Subtracting 881 from 1400, we get the result 519.

Step 10: Now the quotient is 44.1.

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

So the square root of √1950 is approximately 44.16.

The 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 1950 using the approximation method.

Step 1: Now we have to find the closest perfect square of √1950. The smallest perfect square less than 1950 is 1936 (44^2), and the largest perfect square greater than 1950 is 2025 (45^2). √1950 falls somewhere between 44 and 45.

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 (1950 - 1936) ÷ (2025 - 1936) = 14 / 89 ≈ 0.1573. 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 44 + 0.1573 ≈ 44.16, so the square root of 1950 is approximately 44.16.

• 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, which is √16 = 4.

• Irrational number: An irrational number is a number that cannot be written as a ratio of two integers, where the denominator is not zero. For example, √2, √3, and π are irrational numbers.

• Perfect square: A perfect square is an integer that is the square of an integer. For example, 1, 4, 9, 16, and 25 are perfect squares.

• Prime factorization: Prime factorization is the process of expressing a number as a product of its prime factors. For example, the prime factorization of 18 is 2 x 3 x 3.

• Long division method: The long division method is a technique used to find the square root of non-perfect squares by dividing the number into groups and using successive approximation.