Find the square root of 128
The square root of 128 is approximately 11.314
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I apologize for the mistake. The correct square root of 128 is approximately 11.314.
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To find the square root of 128, follow these steps:
1. Begin by making an educated guess. In this case, the square root of 128 is likely to be between 10 and 11.
2. Take the average of your guess and the original number, 128. (10 + 128/10 = 10 + 12.8 = 22.8/2 = 11.4). Our average is 11.4.
3. Divide 128 by your approximation (11.4). (128/11.4 = 11.228).
4. Average your approximation (11.4) with the result of the division (11.228). (11.4 + 11.228/2 = 11.314). Our new average is 11.314.
5. Repeat steps 3 and 4 until you reach the desired level of accuracy.
By following these steps iteratively, you will arrive at a fairly accurate approximation of the square root of 128.
The square root of 128 is approximately 11.314.
To find the square root of 128, we can use the prime factorization of 128 to simplify the calculation.
The prime factorization of 128 is 2^7.
Taking the square root of 2^7, we can divide the exponent by 2 to find the square root:
√(2^7) = 2^(7/2) = 2^(3.5)
Since 2^(3.5) is not a whole number, we can estimate its decimal value.
Estimating 2^(3.5) to be between 2^3 and 2^4:
2^3 = 8
2^4 = 16
Based on this estimation, we can say that the square root of 128 is approximately between 8 and 16.
Let's refine the estimation:
Taking the average of 8 and 16:
(8 + 16) / 2 = 12
Checking if 12 is the correct square root by squaring it:
12^2 = 144
Since 144 is greater than 128, we can conclude that our estimation of 12 is too high.
Let's refine the estimation again:
Taking the average of 8 and 12:
(8 + 12) / 2 = 10
Checking if 10 is the correct square root by squaring it:
10^2 = 100
Since 100 is less than 128, we can conclude that our estimation of 10 is too low.
Let's refine the estimation once more:
Taking the average of 10 and 12:
(10 + 12) / 2 = 11
Checking if 11 is the correct square root by squaring it:
11^2 = 121
Since 121 is less than 128, we can conclude that our estimation of 11 is too low.
Let's refine the estimation again:
Taking the average of 11 and 12:
(11 + 12) / 2 = 11.5
Checking if 11.5 is the correct square root by squaring it:
11.5^2 = 132.25
Since 132.25 is greater than 128, we can conclude that our estimation of 11.5 is too high.
Let's refine the estimation one last time:
Taking the average of 11 and 11.5:
(11 + 11.5) / 2 ≈ 11.25
Checking if 11.25 is the correct square root by squaring it:
11.25^2 ≈ 126.5625
Since 126.5625 is less than 128, we can conclude that our estimation of 11.25 is too low.
Therefore, the square root of 128 is approximately 11.25.