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How can you get the nth root of not perfect square?

Updated: 8/18/2019
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13y ago

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The best way to do this is using a scientific calculator. The calculation is too involved to do with pencil and paper. Note that, for example, the 5th. root of 2 is the same as 2 to the power (1/5).

As to the actual method, a very simple method - albeit somewhat slow - consists of taking the powers of different numbers, until you find one that is close enough. For example, to get the 5th. root of 2 means to find a number that, raised to the 5th. power, is equal to 2. Since 1.15 = 1.61 (less than two) and 1.25 = 2.49 (more than two), the 5th. root of 2 must be between 1.1 and 1.2.

Calculators and computer programs use other methods, that are faster. These methods are based on evaluation of the exponential function (e to the power x) and logarithmic functions (base-e logarithm).

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Q: How can you get the nth root of not perfect square?
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