Square Root of 1316

The square root is the inverse of the square of the number. 1316 is not a perfect square. The square root of 1316 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1316, whereas in the exponential form it is (1316)^(1/2). √1316 ≈ 36.27, 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 1316 is broken down into its prime factors.

Step 1: Finding the prime factors of 1316

Breaking it down, we get 2 x 2 x 3 x 109: 2^2 x 3^1 x 109^1

Step 2: Now we found out the prime factors of 1316. The second step is to make pairs of those prime factors. Since 1316 is not a perfect square, therefore the digits of the number can’t be grouped in pairs. Therefore, calculating 1316 using prime factorization 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 1316, we need to group it as 16 and 13.

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

Step 3: Now let us bring down 16 which is the new dividend. Add the old divisor with the same number 3 + 3, we get 6 which will be our new divisor.

Step 4: The new divisor will be the sum of the dividend and quotient. Now we get 60n as the new divisor, we need to find the value of n.

Step 5: The next step is finding 60n × n ≤ 416. Let's consider n as 6, now 60 x 6 = 360.

Step 6: Subtract 416 from 360, the difference is 56, and the quotient is 36.

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 5600.

Step 8: Now we need to find the new divisor that is 729 because 729 x 7 = 5103.

Step 9: Subtracting 5103 from 5600, we get the result 497.

Step 10: Now the quotient is 36.7.

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

So the square root of √1316 ≈ 36.27.

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 1316 using the approximation method.

Step 1: Now we have to find the closest perfect square of √1316. The smallest perfect square less than 1316 is 1296, and the largest perfect square greater than 1316 is 1369. √1316 falls somewhere between 36 and 37.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula (1316 - 1296) ÷ (1369 - 1296) = 20 ÷ 73 ≈ 0.27. 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 + 0.27 = 36.27.

So the square root of 1316 is approximately 36.27.

• Square root: A square root is the inverse of a square. 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 the principal square root.

• Prime factorization: Prime factorization is the decomposition of a composite number into a product of prime numbers.

• Perfect square: A perfect square is a number that is the square of an integer. For example, 36 is a perfect square because it is 6².