1. Finding square root with counting rods Example: square root of 18983449

2. Place the number in the second row and a rod in the units position of the bottom row, and another in the top row.
Quotient |
Dividend 1 8 9 3 4
Divisor
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3. Move the rod in the bottom row 2 places to the left and the one in the top row 1 place to the left.
Quotient |
Dividend 1 8 9 3 4
Divisor
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4. Move the rod in the bottom row 2 places to the left and the one in the top row 1 place to the left.
Quotient |
Dividend 1 8 9 3 4
Divisor
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5. Replace the rod in the top row by the largest digit whose square does not exceed the number in the second row above the row in the bottom row; also place this number in the third row, under the number in the second row. In this case it is 4.
Quotient |
Dividend 1 8 9 3 4
Divisor
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6. Subtract the square of this digit from the number in the second row above the row in the bottom row.
Quotient 4
Dividend 1 8 9 3
Divisor
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7. Double the number in the third row and move it one place to the right
Double the number in the third row and move it one place to the right. Move the rod in the bottom row 2 places to the right.
Quotient 4
Dividend 2 9 8 3
Divisor
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8. Find the largest digit which when put in the top and third row will give a product not exceeding the number in the second row. In this case, it is 3.
Quotient 4
Dividend 2 9 8 3
Divisor
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9. Subtract the product of this digit and the number in the first row from the second row.
Quotient 4 3
Dividend 2 9 8
Divisor
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10. Add the last digit in the top row to the number in the third row and move one place to the right. Move the rod in the bottom row 2 places to the right.
Quotient 4 3
Dividend 9
Divisor 8
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11. Find the largest digit which when put in the top and third row will give a product not exceeding the number in the second row. In this case, it is 5.
Quotient 4 3
Dividend 9
Divisor 8 6
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12. Subtract the product of this digit and the number in the first row from the second row.
Quotient 4 3 5
Dividend 9
Divisor 8 6
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13. Add the last digit in the top row to the number in the third row and move one place to the right. Move the rod in the bottom row 2 places to the right.
Quotient 4 3 5
Dividend 6 9
Divisor 8
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14. Find the largest digit which when put in the top and third row will give a product not exceeding the number in the second row. In this case, it is 7.
Quotient 4 3 5
Dividend 6 9
Divisor 8 7
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15. Subtract the product of this digit and the number in the first row from the second row.
Quotient 4 3 5 7
Dividend 6 9
Divisor 8
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16. There is no number left in the second row
There is no number left in the second row. The number in the top line is the square root.
Quotient 4 3 5 7
Dividend
Divisor 8
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