Square Root of 1396

The square root is the inverse of the square of the number. 1396 is not a perfect square. The square root of 1396 is expressed in both radical and exponential form. In the radical form, it is expressed as √1396, whereas (1396)^(1/2) in the exponential form. √1396 ≈ 37.349, 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 1396 is broken down into its prime factors.

Step 1: Finding the prime factors of 1396 Breaking it down, we get 2 × 2 × 349: 2² × 349¹

Step 2: Now we found out the prime factors of 1396. The second step is to make pairs of those prime factors. Since 1396 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.

Therefore, calculating 1396 using prime factorization is impractical.

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 1396, we need to group it as 96 and 13.

Step 2: Now we need to find n whose square is less than or equal to 13. We can say n as ‘3’ because 3 × 3 = 9 is lesser than 13. Now the quotient is 3, and after subtracting 9 from 13, the remainder is 4.

Step 3: Now let us bring down 96, which is the new dividend. Add the old divisor 3 with the same number, 3 + 3, we get 6, which will be our new divisor.

Step 4: The new divisor will be 6n. We need to find the value of n.

Step 5: Find 6n × n ≤ 496. Let us consider n as 7, now 67 × 7 = 469.

Step 6: Subtract 469 from 496; the difference is 27, and the quotient is 37.

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 2700.

Step 8: Now we need to find the new divisor; it is 745, because 745 × 3 = 2235.

Step 9: Subtracting 2235 from 2700, we get the result 465.

Step 10: Now the quotient is 37.3.

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

So the square root of √1396 is approximately 37.35.

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 1396 using the approximation method.

Step 1: Now we have to find the closest perfect square of √1396.

The smallest perfect square less than 1396 is 1296, and the largest perfect square greater than 1396 is 1444. √1396 falls somewhere between 36 and 38.

Step 2: Now we need to apply the formula: (Given number - smaller perfect square) / (larger perfect square - smaller perfect square). Going by the formula (1396 - 1296) / (1444 - 1296) = 100 / 148 ≈ 0.676

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 36 + 0.676 ≈ 36.676, so the square root of 1396 is approximately 37.35.

• Square root: A square root is the inverse of a square. For example, 4² = 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: This is the process of expressing a number as the product of its prime factors.

• Long division method: A technique for finding the square root of a number by dividing it into smaller parts and finding each digit of the square root step by step.