Square Root of 1201

The square root is the inverse of the square of the number. 1201 is not a perfect square. The square root of 1201 is expressed in both radical and exponential forms. In the radical form, it is expressed as √1201, whereas (1201)^(1/2) in the exponential form. √1201 ≈ 34.6586, 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 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 1201 is broken down into its prime factors.

Step 1: Finding the prime factors of 1201 Breaking it down, we see 1201 is a prime number itself, so it cannot be factored further.

Step 2: Since 1201 is not a perfect square and cannot be broken into pairs of prime factors, calculating √1201 using prime factorization is not possible.

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 1201, we need to group it as 01 and 12.

Step 2: Now we need to find n whose square is 1. We can say n is ‘1’ because 1 × 1 is less than or equal to 1. The quotient is 1, and after subtracting 1-1, the remainder is 0.

Step 3: Bring down 20, which is the new dividend. Add the old divisor with the same number: 1 + 1 = 2, which will be our new divisor.

Step 4: The new divisor becomes 2n. We need to find the value of n such that 2n × n ≤ 20. Let us consider n as 4, now 2 × 4 × 4 = 32, but 2 × 3 × 3 = 18.

Step 5: Subtract 18 from 20; the difference is 2, and the quotient is 13.

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 200.

Step 7: We need to find the new divisor. Add the last digit of the quotient to the current divisor: 26 + 3 = 29.

Step 8: Find n such that 293n × n ≤ 2000. Consider n as 6, 293 × 6 = 1758.

Step 9: Subtracting 1758 from 2000, we get 242. Step 10: Continue these steps until we get the desired number of decimal places.

So, the square root of √1201 is approximately 34.6586.

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 1201 using the approximation method.

Step 1: Find the closest perfect squares for √1201. The smallest perfect square less than 1201 is 1156, and the largest perfect square greater than 1201 is 1225. √1201 falls somewhere between 34 and 35.

Step 2: Use the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square) to approximate the decimal. (1201 - 1156) / (1225 - 1156) = 45 / 69 ≈ 0.6522 Add 34 to the decimal approximation: 34 + 0.6522 = 34.6522

Thus, the square root of 1201 is approximately 34.6586.

• Square root: A square root is a value that, when multiplied by itself, gives the original number. Example: 5^2 = 25, and the inverse of the square is the square root so √25 = 5.
   
• Irrational number: An irrational number is a number that cannot be expressed as a simple fraction; its decimal goes on forever without repeating.
   
• Prime number: A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
   
• Long division method: A technique used to find the square root of non-perfect squares by dividing the number step by step.
   
• Approximation: The process of finding a value that is close enough to the correct answer, usually with some form of estimation.