Respuesta :

Catya

It depends on what calculator you have. You may find a "Rad' function which will give you the largest square free divisor of the integer input. It may be hidden in in among other useful tool under a "math" key of "app". Again it depends on what calculator you have. Or if you don't have the Rad function (do not mistake for radian mode) there may be a prime factor function which will give you all the prime factors and then you can just multiple them together to get the radical integer.

All scientific and graphing calculators have the ability to find square roots. Usually, the key involved has a square-root symbol: √. The particulars can be found in the manual for your calculator. (Sometimes, a shift operation is required to access that key.)

If you only have a 4-function calculator, you can still get close, but it takes several steps. The basic method is to divide the original number by a guess at its square root, then average that result with the guess to make a new guess. Continue until you have the accuracy you desire.

For example, √17 ≈ 4. Dividing 17 by 4 gives 4.25, and the average of that with 4 is 4.125. Dividing 17 by 4.125 gives 4.121212... and the average of that with 4.125 is 4.12310606... This is good to 5 significant digits. (4.1231).

_____

If you're concerned with roots of index other than 2, you can use a similar method to the above, but it gets more complicated for higher roots. For example, the next guess for a cube root of n is (2/3)x + (1/3)n/x², where x is the present guess.

_____

For calculators with a yˣ key, the value of x can be the reciprocal of the root index. For a 5th root, you would use x=1/5. That is ...

[tex]\displaystyle\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]

_____

You can always use logarithms to find roots. The log of the root is the log of the original number divided by the root index. That is

[tex]\displaystyle\log{\left(\sqrt[n]{x}\right)}=\frac{\log{(x)}}{n}[/tex]