<\/span><\/h2>\nAnother method to find the value of the square root of 2 is by using the long division method.<\/p>\n
Step 1:<\/b> Start by assuming a possible digit for the square root of 2, let’s say 1. Multiply this digit by itself, giving you 1 \u00d7 1 = 1.<\/p>\n
Step 2:<\/b> Subtract this result from 2: 2 – 1 = 1.<\/p>\n
Step 3:<\/b> Bring down the next digit of 2 and double the assumed digit: 1 \u00d7 2 = 2.<\/p>\n
Step 4:<\/b> Now, find the largest digit D that satisfies the inequality D(20D) \u2264 12. In this case, D is 4 as 4(20 + 4) = 96 \u2264 120.<\/p>\n
Step 5:<\/b> Multiply the assumed digit by 2 and add the largest digit D found in the previous step. This gives you 2 \u00d7 1 + 4 = 6.<\/p>\n
Step 6:<\/b> Multiply this result by the combined number obtained in step 5 and subtract it from the number in step 3. This gives you: 1 – 6 = -5.<\/p>\n
Step 7:<\/b> Append the digit D to the assumed number, so the square root of 2 becomes 1.4.<\/p>\n
Step 8:<\/b> Repeat steps 3 to 7 until the desired accuracy is achieved. In this case, the square root of 2 is approximately 1.41421356.<\/p>\n
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