Find the square root of 484 by long division method

Find the square root of 484 by long division method

The correct answer and explanation is:

To find the square root of 484 using the long division method, follow these steps:

Step 1: Group the digits in pairs

Start by grouping the digits of 484 from right to left in pairs. For 484, you would have two groups: 4 and 84.

Step 2: Find the largest number whose square is less than or equal to the first group

In this case, the first group is 4. The largest number whose square is less than or equal to 4 is 2 because 2^2 = 4.

Step 3: Subtract the square of the number from the first group and bring down the next group

Subtract 4 from 4 (the first group) which gives 0. Now, bring down the next pair, which is 84, making the new number 084.

Step 4: Double the number already found and use it as a divisor

Now, double the number already found, which is 2. Doubling gives 4. Write it down, leaving a blank next to it: 4_.

Step 5: Find the next digit

Now, find a digit that, when placed in the blank, makes the divisor and the resulting product less than or equal to 84. The divisor is 40 (after you place the blank), so the number you need to find is the digit ‘2’. If you place 2 in the blank, you get 42, and multiplying 42 by 2 gives 84, which is equal to the remainder.

Step 6: Finish the process

Now, subtract 84 from 84, which gives a remainder of 0. The number you have formed, 22, is the square root of 484.

Final Answer:

The square root of 484 is 22.

Explanation:

This method is essentially a step-by-step approximation process, refining the guess for the square root by checking for divisibility at each stage. It uses the principle of subtracting the squares of the numbers and continually refining the result until a remainder of 0 is achieved. The key steps include dividing, estimating the next digit, and reducing the number progressively by adjusting the divisor.