Square Root of 7744

The square root is the inverse of the square of the number. 7744 is a perfect square. The square root of 7744 is expressed in both radical and exponential form. In the radical form, it is expressed as √7744, whereas (7744)^(1/2) in the exponential form. √7744 = 88, 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. However, the long division method can also be used for any number. Let us now learn the following methods:

• Prime factorization method
• Long division method

The product of prime factors is the prime factorization of a number. Now let us look at how 7744 is broken down into its prime factors.

Step 1: Finding the prime factors of 7744 Breaking it down, we get 2 x 2 x 2 x 2 x 11 x 11: 2^4 x 11^2

Step 2: Now we found out the prime factors of 7744. The second step is to make pairs of those prime factors. Since 7744 is a perfect square, we can pair the digits: (2 x 2) x (2 x 2) x (11 x 11).

Step 3: Taking one factor from each pair gives us the square root: 2 x 2 x 11 = 44.

The long division method is particularly used for non-perfect square numbers, but it can also be used for perfect squares. 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 7744, we group it as 77 and 44.

Step 2: Now we need to find a number whose square is less than or equal to 77. We can use 8 since 8 x 8 = 64. Subtracting 64 from 77 gives us 13.

Step 3: Bring down the next pair, 44, making the new dividend 1344. Add the old divisor with the same number: 8 + 8 = 16, which will be our new divisor.

Step 4: The new divisor will be 160. Find a number n such that (160 + n) x n ≤ 1344. We find n = 8 since 168 x 8 = 1344.

Step 5: Subtracting 1344 from 1344 gives 0. So we have found the square root to be 88.

Students do make mistakes while finding the square root, like forgetting about the negative square root, skipping steps in the long division method, 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. For example, 88^2 = 7744, and the inverse of the square is the square root, which is √7744 = 88.
   
• Perfect square: A perfect square is an integer that is the square of an integer. For example, 7744 is a perfect square because it is 88 squared.
   
• Rational number: A rational number is a number that can be expressed 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, but the positive square root is often used in practical applications. This is known as the principal square root.
   
• Prime factorization: Prime factorization is expressing a number as the product of its prime factors. For example, the prime factorization of 7744 is 2^4 x 11^2.