Square root of 400 by Long …

To find the square root of 400 using long division method, you can follow these steps: 1. Start by grouping the digits in pairs from right to left. Since 400 is a perfect square, it can be written as \(20^2\). So, we group the digits as 4 and 00. 2. Begin with the largest number whose square is less than or equal to 4, which is 2. Write 2 as the quotient and divisor, and place a decimal point after it. 3. Square 2, which equals 4. Subtract 4 from the first group (4). Bring down the next group (00) next to the remainder. 4. Double the quotient (2) to get 4, and write it as the trial divisor. Add a digit to the quotient (let's say 'x') such that 4x multiplied by x is less than or equal to 400. Since \(20^2 = 400\), we know that x should be 0. 5. Multiply the trial divisor (40) by 0, and subtract the result from the number formed by the first two groups (400). This gives you the remainder. 6. Bring down the next pair of zeros (00) and repeat steps 4 and 5 until you have enough decimal places or until you reach the desired level of accuracy. Since 400 is a perfect square, its square root is a whole number, which is 20. So, the square root of 400 by long division method is 20.