Square Root of 6625

The square root is the inverse of the square of the number. 6625 is not a perfect square. The square root of 6625 is expressed in both radical and exponential form. In the radical form, it is expressed as √6625, whereas (6625)^(1/2) in the exponential form. √6625 ≈ 81.414, 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 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 6625 is broken down into its prime factors.

Step 1: Finding the prime factors of 6625. Breaking it down, we get 5 x 5 x 265: 5^2 x 53.

Step 2: Now we found out the prime factors of 6625. The second step is to make pairs of those prime factors. Since 6625 is not a perfect square, therefore, the digits of the number can’t be grouped in pairs.

Therefore, calculating 6625 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 6625, we need to group it as 65 and 6.

Step 2: Now we need to find n whose square is less than or equal to 6. We can say n as '2' because 2 x 2 is 4, which is less than 6. Now the quotient is 2, and after subtracting 4 from 6, the remainder is 2.

Step 3: Now let us bring down 625, which is the new dividend. Add the old divisor with the same number: 2 + 2 = 4, which will be our new divisor.

Step 4: The new divisor will be 4n. We need to find the value of n such that 4n x n ≤ 2625.

Step 5: The next step is finding 4n x n ≤ 2625. Let us consider n as 6; now, 46 x 6 = 276.

Step 6: Subtract 276 from 2625, and the difference is 2349. The new quotient is 26.

Step 7: Since the dividend is less than the new product, we add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 234900.

Step 8: Now we need to find the new number n, such that 526n x n is close to 234900. Let's assume n = 4. Then 5264 x 4 ≈ 21056.

Step 9: Subtracting 21056 from 234900, we get the result 22444.

Step 10: Now the quotient is 81.4.

Step 11: Continue doing these steps until we get two numbers after the decimal point or until the remainder is zero.

So the square root of √6625 ≈ 81.41.

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 6625 using the approximation method.

Step 1: Now we have to find the closest perfect square of √6625.

The smallest perfect square less than 6625 is 6561 (81^2), and the largest perfect square greater than 6625 is 6724 (82^2). √6625 falls somewhere between 81 and 82.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (6625 - 6561) / (6724 - 6561) = 64 / 163 ≈ 0.393.

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 81 + 0.393 = 81.393, so the square root of 6625 is approximately 81.393.

• 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 a principal square root.

• Prime factorization: This is the process of expressing a number as the product of its prime factors.

• Long division method: A systematic method used to find the square root of numbers, especially non-perfect squares, through a series of division steps.