Square Root of 1202

The square root is the inverse of the square of a number. 1202 is not a perfect square. The square root of 1202 can be expressed in both radical and exponential form. In radical form, it is expressed as √1202, whereas in exponential form, it is expressed as (1202)¹/². √1202 ≈ 34.671, 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 1202 is broken down into its prime factors.

Step 1: Finding the prime factors of 1202 Breaking it down, we get 2 x 601: 2¹ x 601¹

Step 2: Now we found out the prime factors of 1202. Since 1202 is not a perfect square, we cannot make pairs of the prime factors.

Therefore, calculating √1202 using prime factorization is not practical.

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 1202, we need to group it as 02 and 12.

Step 2: Now we need to find n whose square is less than or equal to 12. We can say n as ‘3’ because 3 x 3 = 9 is less than 12. Now the quotient is 3, and after subtracting 9 from 12, the remainder is 3.

Step 3: Now let us bring down 02, 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: Now we need to find a digit, say m, such that 6m x m is less than or equal to 302.

Step 5: Let m be 4, then 64 x 4 = 256.

Step 6: Subtract 256 from 302, the difference is 46, and the quotient 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 dividend. Now the new dividend is 4600.

Step 8: Now we need to find the new divisor that is 689 because 689 x 6 = 4134.

Step 9: Subtracting 4134 from 4600, we get the result 466.

Step 10: Now the quotient is 34.6.

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

So the square root of √1202 is approximately 34.671.

The approximation method is another way to find square roots. It is an easy method to estimate the square root of a given number. Now let us learn how to find the square root of 1202 using the approximation method.

Step 1: Find the closest perfect squares around √1202. The smallest perfect square less than 1202 is 1156, and the largest perfect square more than 1202 is 1225. √1202 falls somewhere between 34 and 35.

Step 2: Now apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (1202 - 1156) / (1225 - 1156) = 46 / 69 ≈ 0.667. Adding this to the lower integer value, 34 + 0.667 = 34.667.

So the square root of 1202 is approximately 34.671.

• Square root: A square root is the inverse of squaring a number. Example: 4² = 16, and the square root of 16 is √16 = 4.
   
• Irrational number: An irrational number is a number that cannot be expressed as a simple fraction. Its decimal form is non-repeating and non-terminating.
   
• Principal square root: The positive square root of a number, which is most commonly used in calculations, is called the principal square root.
   
• Decimal: A decimal is a number that includes a fraction represented in a base-10 numeral system, such as 7.86, 8.65, and 9.42.
   
• Prime factorization: This is the process of expressing a number as the product of its prime factors, which are the building blocks of the number.