To find the square root of 64 using long division, you can follow these steps:
1. Start by grouping the digits of 64 into pairs from right to left: 6 and 4.
2. Determine the largest digit, x, such that x * x is less than or equal to 6. In this case, x = 2 since 2 * 2 = 4.
3. Write x on top as the quotient and below it, write x * x (which is 4).
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2 │ 64
4. Subtract x * x (4) from the first pair of digits (6) and bring down the next pair (4) to form a new dividend.
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2 │ 64
4
5. Multiply the quotient (2) by 2 again to get 4 and place it as the divisor of the new dividend.
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2 │ 64
4
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40
6. Determine the largest digit, y, such that y * (20 + y) is less than or equal to 40. In this case, y = 4 since 4 * (20 + 4) = 96, which is greater than 40.
7. Write y next to x in the quotient and below it, write y * (20 + y) (which is 44).
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2 │ 64
44
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20
8. Subtract y * (20 + y) (44) from the 40 to get 20, which becomes the new dividend.
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2 │ 64
44
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20
9. Repeat steps 5 to 8 until the dividend becomes zero, or until you have reached your desired level of accuracy.
In this case, since the dividend has become zero, no further steps are needed.
Thus, the square root of 64 is exactly 8.
Find the square root of 64 by using the long division method
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