Square Root of 1301

The square root is the inverse of the square of the number. 1301 is not a perfect square. The square root of 1301 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1301, whereas (1301)^(1/2) in the exponential form. √1301 ≈ 36.067, 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 1301 is broken down into its prime factors.

Step 1: Finding the prime factors of 1301 1301 is a prime number and cannot be broken down into smaller prime factors. Therefore, calculating 1301 using prime factorization 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 1301, we need to group it as 01 and 13.

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

Step 3: Bring down 01, which makes the new dividend 401. Add the old divisor with the same number 3 + 3 = 6, which will be our new divisor placeholder.

Step 4: Now, we need to find a digit x such that 6x * x ≤ 401. Let us consider x as 6, now 66 * 6 = 396.

Step 5: Subtract 396 from 401, and the remainder is 5.

Step 6: Since the dividend is smaller than the divisor, we add a decimal point to the quotient and bring down 00, making the new dividend 500.

Step 7: Now, find the new divisor that is 606y * y ≤ 5000. Let us consider y as 8, now 608 * 8 = 4864.

Step 8: Subtract 4864 from 5000, and the remainder is 136. Step 9: The quotient is now 36.08. Continue doing these steps until you achieve the desired decimal precision.

So the square root of √1301 ≈ 36.067.

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 1301 using the approximation method.

Step 1: Find the closest perfect squares of √1301. The smallest perfect square less than 1301 is 1296, and the largest perfect square greater than 1301 is 1369. √1301 falls somewhere between 36 and 37.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula (1301 - 1296) / (1369 - 1296) ≈ 0.067 Using the formula, we identified the decimal point of our square root. Add this value to the smaller whole number: 36 + 0.067 = 36.067. Thus, the square root of 1301 is approximately 36.067.

• Square root: A square root is the inverse of a square. Example: 36^2 = 1296 and the inverse of the square is the square root, which is √1296 = 36.

• 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.

• Prime number: A prime number has only two distinct positive divisors: 1 and itself. Example: 1301 is a prime number.

• Perfect square: A perfect square is a number that can be expressed as the square of an integer. Example: 36 is a perfect square because it can be written as 6^2.

• Decimal: If a number has a whole number and a fraction in a single number, then it is called a decimal. For example: 7.86, 8.65, and 9.42 are decimals.