Square Root of 1153

The square root is the inverse of the square of the number. 1153 is not a perfect square. The square root of 1153 is expressed in both radical and exponential form. In the radical form, it is expressed as √1153, whereas in the exponential form it is (1153)^(1/2). √1153 ≈ 33.9479, 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, for non-perfect square numbers, 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 1153 is broken down into its prime factors.

Step 1: Finding the prime factors of 1153 Breaking it down, we find 1153 is a product of 1 x 1153, indicating it is a prime number itself. Since 1153 is not a perfect square and does not have pairs of prime factors, calculating √1153 using prime factorization is not feasible.

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 1153, we need to group it as 53 and 11.

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

Step 3: Bring down 53 to make the new dividend 253. Add the old divisor (3) with the same number to get 6, which will be our new divisor.

Step 4: The new divisor is 6n. We need to find the value of n such that 6n x n ≤ 253. Let us consider n as 4, now 64 x 4 = 256, which is more than 253. So, try n as 3, 63 x 3 = 189.

Step 5: Subtract 189 from 253, the difference is 64, and the quotient becomes 33.

Step 6: Add a decimal point and bring down two zeros to make it 6400.

Step 7: Find the new divisor, now 66n. If n = 9, then 669 x 9 = 6021.

Step 8: Subtract 6021 from 6400, and the remainder is 379. Now the quotient is 33.9.

Step 9: Continue this process until you reach the desired decimal places. The square root of √1153 is approximately 33.95.

The approximation method is an easy way to find the square root of a given number. Now, let us learn how to find the square root of 1153 using the approximation method.

Step 1: Find the closest perfect squares of √1153. The smallest perfect square less than 1153 is 1089 (√1089 = 33), and the largest perfect square more than 1153 is 1156 (√1156 = 34). √1153 falls between 33 and 34.

Step 2: Apply the formula (Given number - smallest perfect square) ÷ (Greater perfect square - smallest perfect square). Using the formula: (1153 - 1089) ÷ (1156 - 1089) = 64 ÷ 67 ≈ 0.955 Add this decimal to the smaller integer: 33 + 0.955 = 33.955 So, the square root of 1153 is approximately 33.955.

• Square root: A square root is the inverse of squaring a number. For example, 4² = 16, and the inverse is √16 = 4.

• Prime number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

• Irrational number: An irrational number cannot be written as a simple fraction, i.e., in the form of p/q where q is not equal to zero and p and q are integers.

• Approximation: Estimating a value that is close to, but not exactly, the true value. Used for non-perfect squares to find square roots.

• Long division method: A technique for dividing numbers step by step, which can be used to find square roots of non-perfect squares.