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What are Roots?

Not only are roots the subsurface, nutrient gather appendages of plants! Roots are also way to determine how many times a number, multiplied by itself, can go into a larger number. This probably sounds a lot like multiplication or division, which is good because they are related!

The Square Root
The most popular root, the square root, is asking a simple question "What number multiplied by itself equals the given number?"


This is asking "What number multiplied by itself equals 4?" The answer, of course, is 2!

Another example of this type of problem would be:
Similar to the above, this is asking "What number multiplied by itself equals 16?" The answer here, is 4, since 4 * 4 = 16!

There are roots that are not always quite so perfect. Consider the following:

The square root of 14. What number multipled by itself equals 14? This one is a bit trickier. 2*2 is 4; 3*3 is 9; 4*4 is 16. There is not a whole number that fits! But we do know that the square root is between 3 and 9. There are manual methods to determine the answer to these, as shown in Using Roots and Squares, but for this time, we will use a calculator.

By using a calculator, we find that the square root is: 3.7416573867739413855837487323165. Wow! You will almost never be required to find a number so long, instead, you will round your answer. Let's round to 3.74.

To check our answer, we can square it to see if we get close to the number we're trying to find the root of:

3.74 * 3.74 = 13.9876

And that's very close to 14!

If we were to use our longer answer, we would get:

3.7416573867739413855837487323165 * 3.7416573867739413855837487323165 = 13.999999999999999999999999999996

And that answer is closer to 14, but it is not very easy on the eyes.


Find another math lesson at the Math Lesson and Tutorial Center!


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