Q: How do you calculate nth root?

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The easiest way to do this is with a calculator. Anyway, the definitions are as follows. x to the power 1/2 is the square root of x, x to the power 1/3 is the cubic root of x, and in general, x to the power 1/n is the nth. root of x. If you also have a number other than one in the numerator: For example, to calculate x to the power 3/5 you first raise x to the power 3, then take the fifth root of the result. You can also do it the other way: first calculate the fifth root, then raise to the third power. In general, to calculate x to the power m/n, you take the nth root, then raise the result to the power m.

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.

yes the nth root of zero is always zero

Assuming that you mean the nth. root: two - a negative and a positive root.

To calculate the geometric mean, multiply together all the values and take the nth root, where n is the number of values multiplies together: 2 values → square root, 3 values → cube root, etc. ie geometric_mean = (product_of_n_values)1/n geometric_mean(12) = 121/1 = 121 = 12.

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The nth root is unstoppable. You must sit back and wait. Hopefully you will survive it as it takes its deadly course.

The easiest way to do this is with a calculator. Anyway, the definitions are as follows. x to the power 1/2 is the square root of x, x to the power 1/3 is the cubic root of x, and in general, x to the power 1/n is the nth. root of x. If you also have a number other than one in the numerator: For example, to calculate x to the power 3/5 you first raise x to the power 3, then take the fifth root of the result. You can also do it the other way: first calculate the fifth root, then raise to the third power. In general, to calculate x to the power m/n, you take the nth root, then raise the result to the power m.

You seem to be unaware of the fact that you can obtain the answer easily by using the scientific calculator that comes as part of your computer. In general the nth root is extremely difficult to find.

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.

The radical symbol, otherwise known as the "square root sign", lets you take the nth root of any number.Any number can be placed above, and slightly to the left, of the square root sign, to indicate the nth root. For example, the cube root of 27 is 3.The number inside the square root sign (that which you are finding the square root of), is called the radicand.

yes the nth root of zero is always zero

The nth root of a number is a number such that if you multiply it by itself (n-1) times you get the number. Or if you multiply 1 by it n times. Many definitions get this wrong due to sloppy use of the language.So if y^n = x then the nth root of x is y.x^(a/b) is the bth root of x^a or, equivalently, it is (bth root of x)^a. If mental calculation is required then the second form is easier to use because it means you are dealing with smaller number. For example, 16^(3/4) can be calculated as (4th root of 16)^3 = 2^3 = 8. Not too difficult. But the alternative method would be to calculate the 4th root of 16^3 = the fourth root of 4096. Not something most people would wish to tackle.A negative root is simply the reciprocal. Thus x^(-a) is simply 1/(x^a).

Assuming that you mean the nth. root: two - a negative and a positive root.

To calculate the geometric mean, multiply together all the values and take the nth root, where n is the number of values multiplies together: 2 values → square root, 3 values → cube root, etc. ie geometric_mean = (product_of_n_values)1/n geometric_mean(12) = 121/1 = 121 = 12.

You can't prove this proposition because it isn't true.Proof: the fifth root of 1024 is 4, and 4 is not irrational.It is true that, when N is an integer greater than 1, the Nth root of any integer greater than 1 is either an integer orirrational, but that's a different matter.

The geometric mean is the nth root of the product of the numbers. So this means (pun intended) multiply the numbers together and then take their nth root. Let's look at 2, 4, and 8 . Their product is 64 and the cube ( 3rd) root of 64 is 4. Of course, most of the time, the answer will not be rational.

The nth root of x2 can be expressed as: x2/n Thinking of it that way, we can see that no, it can't always exist - but almost always. The only condition in which it can't exist is when n = 0, as that would give us division by zero.