Solving For Nth Roots - How To Solve For, Calculate, Or Find The Nth Root Of A Number

In this video we discuss how to solve for, or find the nth root of a number using a calculator and using excel. We go through what an nth root is, and also go through a detailed example.

Transcript/notes
Let’s say that we want to find the 5th root of 42. What this is asking is what number times itself 5 times will equal 42.

For instance, 2 times itself 5 times. 2 times 2, times 2, times 2, times 2 equals 32. So, the 5th root of 32 equals 2.

When solving for nth roots, or even for square roots, technology can dramatically help. We are going to go through this using a basic calculator and then using excel.

Using a basic calculator, you type the number under the radical sign in, in this case the number 42. Next, you press the radical sign 12 times. Next, you subtract 1 and then press the equals sign. Next, you divide by the root index, the number outside of the radical sign, and then press the equals sign. Next, you add 1 and press the equals sign. Next, you press the multiplication sign then the equals sign 12 times. So, times, then equals 12 times. And we get an answer of 2.112352619. Using this method isn’t exactly accurate, I have found that it is typically accurate to the hundredths column.

Using excel, the way it is written is, equals sign, the number under the radical sign, this carrot sign, which is shift 6, open parenthesis, the number 1, forward slash, the number of the root, which is called the root index, and then closed parenthesis. In our example of the 5th root of 42, it would be, 42, carrot symbol, open parenthesis, 1, forward slash, 5, closed parenthesis. And the answer is 2.112 rounded off.

So, if we multiply 2.112 times itself 5 times, we should get an answer close to 42. And as you can see on the screen this is correct, I did get slightly more, but that was because I rounded off to 2.112.

And that is how to calculate the nth root of a number.

Timestamps
0:00 What is an nth root?
0:28 Using a basic calculator to solve for nth roots
1:36 Using excel to solve for nth roots