Here are a few examples:
When you know the area of a square and want its side length.
When you know the volume of a cube and want its side length.
When you know the area of a circle and want its radius or diameter.
When you know the volume of a sphere and want its radius or diameter.
When you know the fixed [compound] interest rate for some investment and want to know how long it will take to double, treble or grow to some fixed amount.
When you know the half-life of some radioactive substance and want to know how long it will take before the quantity remaining has dropped to a specified level - possibly below a safety threshold.
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If your calculator has an exponentiation function, simply raise the number to the power of .5 Remember this trick: the nth root of X = X ^ (1/n)
The nth root of a number is that number which when raised to the nth power (ie when multiplied by itself n times) results in the number. When n=2, it is the square root of the number; when n=3 it is the cube root of the number. To find the nth root of a number, an electronic calculator can be used, using the nth root button [x√y] (though more recent calculators replace the x and y by boxes) viz: <n> [x√y] [2] [4] [4] [=] or with the more recent calculators: [#√#] <n> [Navigate →] [2] [4] [4] [=] where <n> is the nth root, eg for 2nd root (square roots) enter [2]; and the # is being used to represent a box on the keys of the more recent calculator. Considering the rules for indices, the nth root is the the number to the power of 1/n, ie 244^(1/n), thus the calculation can be done using the power button: [2] [4] [4] [^] [(] [1] [÷] <n> [)] [=] With the more recent calculators, the power button is pressed first, the 244 entered, the navigate-right key pressed (to get in to the power part of the input) and then the n entered.
Assuming that you mean the nth. root: two - a negative and a positive root.
The nth triangulat number is n*(n+1)/2 The 100th is 100*101/2 = 5050
The nth even number is 2n...