Square Root of 1369

The square root is the inverse of the square of the number. 1369 is a perfect square. The square root of 1369 is expressed in both radical and exponential form. In the radical form, it is expressed as √1369, whereas in exponential form it is expressed as (1369)^(1/2). √1369 = 37, which is a rational number because it can 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. Since 1369 is a perfect square, we can use the prime factorization method. However, for non-perfect square numbers, long-division and approximation methods 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 1369 is broken down into its prime factors.

Step 1: Finding the prime factors of 1369

Breaking it down, we get 37 x 37: 37^2

Step 2: Now we found out the prime factors of 1369. Since 1369 is a perfect square, the digits of the number can be grouped in pairs. Therefore, calculating 1369 using prime factorization is straightforward, and the square root is 37.

The long division method can also be used for 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 1369, the grouping is not needed as it naturally forms pairs.

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

Step 3: Bring down 69, which is the new dividend. Double the quotient to get the new divisor, 6.

Step 4: The new divisor is now 6n. Find the largest n such that 6n * n is less than or equal to 469.

Step 5: Try n = 7, so 67 x 7 = 469.

Step 6: Subtract 469 from 469, the remainder is 0, and the quotient is 37. Therefore, the square root of 1369 is 37.

The approximation method is another method for finding the square roots, and it is an easy method to find the square root of a given number. However, since 1369 is a perfect square, this method is not necessary.

Students do make mistakes while finding the square root, such as forgetting about the negative square root, skipping long division methods, etc. Now let us look at a few of those mistakes that students tend to make in detail.

• Square root: A square root is the inverse of a square. Example: 6^2 = 36, and the inverse of the square is the square root, that is, √36 = 6.

• Rational number: A rational number is a number that can be written in the form of p/q, where q is not equal to zero and p and q are integers.

• Perfect square: A perfect square is an integer that is the square of an integer. Example: 36 is a perfect square because it is 6^2.

• Integer: An integer is a whole number that can be positive, negative, or zero. Examples: -5, 0, 3, 4.

• Decimal: If a number has a whole number and a fractional part in a single number, then it is called a decimal. Examples: 7.86, 8.65, 9.42.