Square Root of 3796

The square root is the inverse of the square of the number. 3796 is not a perfect square. The square root of 3796 is expressed in both radical and exponential form. In the radical form, it is expressed as √3796, whereas (3796)¹/² in the exponential form. √3796 ≈ 61.583, 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 3796 is broken down into its prime factors.

Step 1: Finding the prime factors of 3796 Breaking it down, we get 2 x 2 x 13 x 73: 2² x 13¹ x 73¹

Step 2: Now we have found the prime factors of 3796. Since 3796 is not a perfect square, we cannot group all digits into pairs.

Therefore, calculating 3796 using prime factorization alone 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 3796, we need to group it as 96 and 37.

Step 2: Now we need to find n whose square is close to 37. We can say n is 6 because 6 * 6 = 36, which is lesser than or equal to 37. Now the quotient is 6, and after subtracting 36 from 37, the remainder is 1.

Step 3: Now let us bring down 96, which makes the new dividend 196. Add the old divisor with the same number, 6 + 6, we get 12, which will be our new divisor.

Step 4: The new divisor is now 12n. We need to find the value of n such that 12n * n ≤ 196. Let us consider n as 1, now 12 * 1 * 1 = 12.

Step 5: Subtract 12 from 196; the difference is 184, and the quotient becomes 61.

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 zeros to the dividend. Now the new dividend is 18400.

Step 7: Now we need to find the new digit for the divisor, which is approximately 58, because 1218 * 1 = 1218.

Step 8: Subtracting 1218 from 18400 gives the result 17182.

Step 9: Continue doing these steps until we get two numbers after the decimal point. Suppose there are no decimal values; continue until the remainder is zero.

So the square root of √3796 ≈ 61.583.

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 3796 using the approximation method.

Step 1: Now we have to find the closest perfect squares to √3796. The smallest perfect square near 3796 is 3721 (which is 61²), and the largest perfect square is 3844 (which is 62²). √3796 falls somewhere between 61 and 62.

Step 2: Now we need to apply the formula that is (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Going by the formula, (3796 - 3721) / (3844 - 3721) = 75/123 ≈ 0.61. 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 61 + 0.61 = 61.61, so the square root of 3796 is approximately 61.61.

• Square root: A square root is the inverse of a square. Example: 4² = 16, and the inverse of the square is the square root, which 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 the positive square root that has more prominence due to its uses in the real world. That is the reason it is also known as a principal square root.
   
• Perfect square: A perfect square is an integer that is the square of an integer. For example, 16 is a perfect square because it is 4².
   
• Approximation: Approximation is a method to find a value that is close to the exact value. For example, √3796 ≈ 61.583 is an approximation.