Square Root of 1300

The square root is the inverse of the square of the number. 1300 is not a perfect square. The square root of 1300 is expressed in both radical and exponential form. In the radical form, it is expressed as, √1300, whereas (1300)^(1/2) in the exponential form. √1300 ≈ 36.0555, 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 1300 is broken down into its prime factors:

Step 1: Finding the prime factors of 1300

Breaking it down, we get 2 x 2 x 5 x 5 x 13: 2^2 x 5^2 x 13

Step 2: Now we found out the prime factors of 1300. The second step is to make pairs of those prime factors. Since 1300 is not a perfect square, the digits of the number can’t be grouped completely in pairs. Therefore, calculating √1300 using prime factorization is not straightforward.

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 1300, we need to group it as 00 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 x 3 = 9, which is less than 13. Now the quotient is 3, and after subtracting 9 from 13, the remainder is 4.

Step 3: Now let us bring down 00, making the new dividend 400. Add the old divisor with the same number 3 + 3 to get 6, which will be our new divisor.

Step 4: The new divisor will be 60, and we need to find the value of n such that 60n × n ≤ 400. Let us consider n as 6. Now, 60 x 6 = 360.

Step 5: Subtract 360 from 400; the difference is 40, and the quotient thus far is 36.

Step 6: Since the dividend is less than the new divisor, we add a decimal point and bring down two zeros, making the new dividend 4000.

Step 7: Now, calculate a new divisor, 721, because 721 x 5 = 3605.

Step 8: Subtracting 3605 from 4000 gives us a remainder of 395.

Step 9: Continue these steps until you have the desired precision. The square root of √1300 is approximately 36.0555.

The approximation method is another method for finding square roots, and it is an easy method to find the square root of a given number. Let us learn how to find the square root of 1300 using the approximation method.

Step 1: Now we have to find the closest perfect square of √1300. The smallest perfect square less than 1300 is 1225, and the largest perfect square greater than 1300 is 1369. √1300 falls somewhere between 35 and 37.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) Using the formula (1300 - 1225) ÷ (1369 - 1225) = 75/144 ≈ 0.52 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 + 0.0555 = 36.0555, so the square root of 1300 is approximately 36.0555.

• 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.

• Prime factorization: The process of expressing a number as the product of its prime factors. For example, the prime factorization of 1300 is 2^2 x 5^2 x 13.

• Long division method: A method used to find the square root of non-perfect squares by dividing the number into smaller parts and solving step by step.