The focus so far has been on similar triangles but there are also theorems that deal with similar
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First step: partition the number you want to square root into a block of 2 digits, starting from the last digit (first diagram)
Second step: As our number is a five-digits, we ends up with 2 28 01. Pick a number that could be squared to get the first partition, 2. This number is 1, since 1×1=1
Third step: Write 1 on the top and on the side, as shown in the second graph
Fourth step: Double the number on the side, which is 1+1=2 and use this number as the first digit for the next multiplier. Meanwhile, subtract 1 from 2 inside the root sign to get 1, then pull the other two digits, 28
Fifth step: We need a value in the boxes that when we multiply together will give a number less than 128. We choose 5 as 25×5=125
Sixth step: Subtract 125 from 128 to give 3, and as the same concept with long division, bring down the 0 and the 1. So we have 301
Seventh step: Add 5 to the multiplier on the left, so 20+5=30, which we will use on the side as the hundred and ten digits.
Final step: Find a number to fit in the boxes. We choose 1 since 301×1=301
And hence the square root of 228801 is 151
Second step: As our number is a five-digits, we ends up with 2 28 01. Pick a number that could be squared to get the first partition, 2. This number is 1, since 1×1=1
Third step: Write 1 on the top and on the side, as shown in the second graph
Fourth step: Double the number on the side, which is 1+1=2 and use this number as the first digit for the next multiplier. Meanwhile, subtract 1 from 2 inside the root sign to get 1, then pull the other two digits, 28
Fifth step: We need a value in the boxes that when we multiply together will give a number less than 128. We choose 5 as 25×5=125
Sixth step: Subtract 125 from 128 to give 3, and as the same concept with long division, bring down the 0 and the 1. So we have 301
Seventh step: Add 5 to the multiplier on the left, so 20+5=30, which we will use on the side as the hundred and ten digits.
Final step: Find a number to fit in the boxes. We choose 1 since 301×1=301
And hence the square root of 228801 is 151