Square Root of 1612

The square root is the inverse of the square of the number. 1612 is not a perfect square. The square root of 1612 is expressed in both radical and exponential form. In the radical form, it is expressed as √1612, whereas (1612)^(1/2) in the exponential form. √1612 ≈ 40.149, 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 1612 is broken down into its prime factors.

Step 1: Finding the prime factors of 1612 Breaking it down, we get 2 x 2 x 13 x 31: 2^2 x 13 x 31

Step 2: Now we have found the prime factors of 1612. The second step is to make pairs of those prime factors. Since 1612 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.

Therefore, calculating 1612 using prime factorization is not straightforward for finding exact square roots.

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 1612, we need to group it as 12 and 16.

Step 2: Now we need to find n whose square is less than or equal to 16. We can say n is 4 because 4 x 4 = 16. Now the quotient is 4, and the remainder is 0 after subtracting 16 from 16.

Step 3: Now let us bring down 12, which is the new dividend. Add the old divisor with the same number 4 + 4, we get 8, which will be our new divisor.

Step 4: The new divisor will be 8n. We need to find the value of n.

Step 5: The next step is finding 8n x n ≤ 12. Let us consider n as 1, now 8 x 1 x 1 = 8.

Step 6: Subtract 12 from 8, the difference is 4, and the quotient is 41.

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 400.

Step 8: Now we need to find the new divisor that is 82 because 82 x 4 = 328.

Step 9: Subtracting 328 from 400, we get the result 72.

Step 10: Now the quotient is 40.1.

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 √1612 ≈ 40.15.

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 1612 using the approximation method.

Step 1: Now we have to find the closest perfect square of √1612.

The smallest perfect square less than 1612 is 1600, and the largest perfect square greater than 1612 is 1681.

√1612 falls somewhere between 40 and 41.

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 (1612 - 1600) / (1681 - 1600) = 12 / 81 ≈ 0.148.

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 40 + 0.148 ≈ 40.148.

So the square root of 1612 is approximately 40.148.

• 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 a principal square root.
   
• Prime factorization: The expression of a number as the product of its prime factors.
   
• Perfect square: A perfect square is a number that is the square of an integer. For example, 16 is a perfect square because it is the square of 4.