Square Root of 1184

The square root is the inverse of the square of the number. 1184 is not a perfect square. The square root of 1184 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1184, whereas (1184)^(1/2) in the exponential form. √1184 ≈ 34.4093, 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 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 1184 is broken down into its prime factors.

Step 1: Finding the prime factors of 1184 Breaking it down, we get 2 x 2 x 2 x 2 x 2 x 37: 2^5 x 37

Step 2: Now we found out the prime factors of 1184. The second step is to make pairs of those prime factors. Since 1184 is not a perfect square, therefore the digits of the number can’t be grouped in pairs.

Therefore, calculating 1184 using prime factorization gives an approximate value.

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 1184, we need to group it as 84 and 11.

Step 2: Now we need to find n whose square is close to 11. We can say n is '3' because 3 x 3 = 9 which is lesser than or equal to 11. Now the quotient is 3 after subtracting 11 - 9, the remainder is 2.

Step 3: Now let us bring down 84 which is the new dividend. 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 (6n), and we need to find the value of n.

Step 5: The next step is finding 60n × n ≤ 284; let us consider n as 4, now 60 x 4 = 240.

Step 6: Subtract 284 from 240, the difference is 44.

Step 7: 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 4400.

Step 8: Now we need to find the new divisor that is 698 because 698 x 6 = 4188.

Step 9: Subtracting 4188 from 4400, we get the result 212.

Step 10: Now the quotient is 34.4.

Step 11: Continue doing these steps until we get two numbers after the decimal point. Suppose if there are no decimal values, continue till the remainder is zero.

So the square root of √1184 is approximately 34.409.

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 1184 using the approximation method.

Step 1: Now we have to find the closest perfect squares to √1184. The smallest perfect square less than 1184 is 1156 (34^2), and the largest perfect square greater than 1184 is 1296 (36^2). √1184 falls somewhere between 34 and 36.

Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1184 - 1156) ÷ (1296 - 1156) = 28 / 140 ≈ 0.2. 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 34 + 0.2 = 34.2.

So the square root of 1184 is approximately 34.409.

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

• Long division method: The long division method is a technique used to find the square root of non-perfect squares by using systematic division and subtraction steps.