Square Root of 1168

The square root is the inverse of the square of the number. 1168 is not a perfect square. The square root of 1168 is expressed in both radical and exponential form. In the radical form, it is expressed as √1168, whereas (1168)^(1/2) in the exponential form. √1168 ≈ 34.175, 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 1168 is broken down into its prime factors.

Step 1: Finding the prime factors of 1168 Breaking it down, we get 2 x 2 x 2 x 2 x 73: 2^4 x 73^1

Step 2: Now we have found the prime factors of 1168. The second step is to make pairs of those prime factors. Since 1168 is not a perfect square, the digits of the number can’t be grouped into pairs. Therefore, calculating 1168 using prime factorization is not possible to find an integer result.

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, group the numbers from right to left. In the case of 1168, we group it as 68 and 11.

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

Step 3: Bring down 68, which is the new dividend. Add the old divisor with the quotient, 3 + 3 = 6, which becomes the new divisor.

Step 4: We now have 26 as the new divisor. Find n such that 26n x n is less than or equal to 268.

Step 5: Let's consider n as 9, then 26 x 9 = 234

Step 6: Subtract 234 from 268; the difference is 34.

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 remainder. The new dividend is 3400.

Step 8: The new divisor becomes 68 (from 260 + 8) because 681 x 5 approximates 3400.

Step 9: Subtracting 3405 from 3400, we get a result of 5.

Step 10: Now the quotient is approximately 34.175.

The approximation method is another method for finding the 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 1168 using the approximation method.

Step 1: Find the closest perfect squares around √1168. The closest perfect squares to 1168 are 1156 (34^2) and 1225 (35^2). √1168 falls between 34 and 35.

Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula: (1168 - 1156) / (1225 - 1156) ≈ 0.175 Adding this to 34, we get 34 + 0.175 = 34.175. So, the square root of 1168 is approximately 34.175.

• 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.

• Principal square root: A number has both positive and negative square roots; however, the positive square root is more prominent due to its uses in the real world. That is the reason it is also known as the principal square root.

• Approximation method: A method used to estimate the square root of non-perfect squares by finding the closest perfect squares around the number.

• Prime factorization: The process of breaking down a number into its basic prime number components, which is often used to simplify square roots.