Square Root of 1925

The square root is the inverse of the square of the number. 1925 is not a perfect square. The square root of 1925 is expressed in both radical and exponential form. In the radical form, it is expressed as √1925, whereas (1925)^(1/2) in exponential form. √1925 ≈ 43.87, 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 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 1925 is broken down into its prime factors.

Step 1: Finding the prime factors of 1925 Breaking it down, we get 5 x 5 x 7 x 11: 5^2 x 7 x 11

Step 2: Now we found the prime factors of 1925. The second step is to make pairs of those prime factors. Since 1925 is not a perfect square, the digits of the number can’t be grouped in pairs.

Therefore, calculating √1925 using prime factorization directly is not possible.

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 1925, we need to group it as 25 and 19.

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

Step 3: Now let us bring down 25, 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 with a placeholder is 80, and we need to find the value of n such that 80n x n is less than or equal to 325. Let us consider n as 4, now 80 x 4 = 320.

Step 5: Subtract 325 from 320, the difference is 5, and the quotient is 44.

Step 6: 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 500.

Step 7: Now we need to find the new divisor, which becomes 880. We find n such that 880n x n is less than or equal to 5000.

Step 8: Through trial, we find that n is 5 because 880 x 5 = 4400.

Step 9: Subtracting 4400 from 5000, we get the result 600.

Step 10: Now the quotient is 43.5

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

So the square root of √1925 is approximately 43.87.

The approximation method is another method for finding 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 1925 using the approximation method.

Step 1: Now we have to find the closest perfect square of √1925. The smallest perfect square less than 1925 is 1849 (43^2) and the largest perfect square greater than 1925 is 2025 (45^2). √1925 falls somewhere between 43 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, (1925 - 1849) / (2025 - 1849) = 76 / 176 ≈ 0.432.

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

The next step is adding the value we got initially to the decimal number which is 43 + 0.432 ≈ 43.87, so the square root of 1925 is approximately 43.87.

• 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; however, it is always the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as the principal square root.

• Perfect square: A perfect square is an integer that is the square of an integer. For example, 16 is a perfect square because it is 4 squared.

• Long division method: A method used to find the square root of a number by dividing the number into groups and estimating each digit of the square root step by step.