Square Root of 8800

The square root is the inverse of the square of the number. 8800 is not a perfect square. The square root of 8800 is expressed in both radical and exponential form. In the radical form, it is expressed as √8800, whereas (8800)^(1/2) in the exponential form. √8800 ≈ 93.808, 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 often used for perfect square numbers. However, for non-perfect square numbers like 8800, the long-division method and approximation method are typically 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 8800 is broken down into its prime factors.

Step 1: Finding the prime factors of 8800

Breaking it down, we get 2 x 2 x 2 x 2 x 5 x 5 x 11: 2^4 x 5^2 x 11

Step 2: We found the prime factors of 8800. The second step is to make pairs of those prime factors. Since 8800 is not a perfect square, the digits of the number can’t be grouped into pairs for all factors. Therefore, calculating 8800 using prime factorization directly to get a perfect square 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 8800, we need to group it as 88 and 00.

Step 2: Now, we need to find n whose square is ≤ 88. We can say n is ‘9’ because 9 x 9 = 81, which is less than 88. The quotient is 9, and after subtracting, the remainder is 7.

Step 3: Now, let us bring down 00, which is the new dividend. Add the old divisor with the same number 9 + 9 to get 18, which will be our new divisor.

Step 4: We need to find n such that 18n × n ≤ 700. Let us consider n as 3, so 183 x 3 = 549.

Step 5: Subtract 549 from 700, and the difference is 151. The quotient is now 93.

Step 6: Since the dividend is less than the divisor, we need to add a decimal point. Adding the decimal point allows us to add two zeroes to the dividend. Now the new dividend is 15100.

Step 7: Now, we need to find the new divisor, which is 938, because 938 x 8 = 15008.

Step 8: Subtracting 15008 from 15100 gives us the result 92.

Step 9: Now the quotient is 93.8.

Step 10: Continue doing these steps until we get two numbers after the decimal point. If there are no decimal values, continue until the remainder is zero.

So the square root of √8800 ≈ 93.80

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 8800 using the approximation method.

Step 1: First, find the closest perfect squares to √8800. The smallest perfect square less than 8800 is 8649, and the next perfect square greater than 8800 is 8836. √8800 falls somewhere between 93 and 94.

Step 2: Now we need to apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square).

Using the formula: (8800 - 8649) / (8836 - 8649) = 151 / 187. This gives approximately 0.808. Adding the whole part gives us 93 + 0.808 = 93.808. So the square root of 8800 ≈ 93.808.

• Square root: A square root is the inverse of a square. For 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.
   
• Perfect square: A perfect square is a number that is the square of an integer. For example, 49 is a perfect square since it is 7 squared.
   
• Long division method: A technique used to find the square root of non-perfect squares by dividing the number into parts.
   
• Prime factorization: This method involves expressing a number as the product of its prime factors.