Square Root of 996

The square root is the inverse of the square of the number. 996 is not a perfect square. The square root of 996 is expressed in both radical and exponential form. In the radical form, it is expressed as √996, whereas (996)^(1/2) in the exponential form. √996 ≈ 31.542, 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, methods like 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 996 is broken down into its prime factors: Step 1: Finding the prime factors of 996 Breaking it down, we get 2 × 2 × 3 × 83: 2^2 × 3^1 × 83^1 Step 2: Now we have found out the prime factors of 996. The second step is to make pairs of those prime factors. Since 996 is not a perfect square, the digits of the number can’t be grouped into pairs for all factors. Therefore, calculating 996 using prime factorization involves approximating or using other methods.

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 996, we group it as 96 and 9. Step 2: Now we need to find n whose square is less than or equal to 9. We choose n as ‘3’ because 3^2 = 9. The quotient is 3, and the remainder is 0. Step 3: Bring down 96, which is the new dividend. Add the old divisor with the same number: 3 + 3 = 6, which will be our new divisor. Step 4: Find 6n such that 6n × n is less than or equal to 96. We try n = 1, so 61 × 1 = 61. Step 5: Subtract 61 from 96; the difference is 35, and the quotient is 31. Step 6: Since the dividend is less than the divisor, add a decimal point, allowing us to add two zeroes to the dividend. The new dividend is 3500. Step 7: Find the new divisor, which is 629, because 629 × 5 = 3145. Step 8: Subtracting 3145 from 3500, we get the result 355. Step 9: The quotient is now 31.5. Step 10: Continue these steps until we achieve the desired precision. The square root of √996 is approximately 31.542.

The approximation method is another way to find square roots. It is an easy method to find the square root of a given number. Let us learn how to find the square root of 996 using the approximation method. Step 1: Find the closest perfect square of √996. The smallest perfect square less than 996 is 961, and the largest perfect square more than 996 is 1024. √996 falls somewhere between 31 and 32. Step 2: Apply the formula: (Given number - smallest perfect square) / (Greater perfect square - smallest perfect square). Using the formula (996 - 961) / (1024 - 961) = 35 / 63 ≈ 0.556. Adding the value to the lower integer, 31 + 0.556 ≈ 31.556, so the square root of 996 is approximately 31.556.

Square root: A square root is the inverse operation of squaring a number. Example: 4^2 = 16, so the square root is √16 = 4. Irrational number: An irrational number is a number that cannot be written as a simple fraction, like √996, which cannot be expressed as p/q where p and q are integers and q ≠ 0. Principal square root: Although a number has both positive and negative square roots, the principal square root refers to the non-negative one, which is commonly used in real-world applications. Approximation: This refers to finding a value that is close enough to the right answer, usually with a specified degree of accuracy. For example, √996 ≈ 31.542. Long division method: A step-by-step division process used to find square roots of non-perfect squares by approximating to the desired decimal places.