How to Find Radicals From Decimals

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How to Convert a Decimal Into a Radical....5

You can find radicals from decimals in a very specific way. Find radicals from decimals with help from an expert in mathematics in this free video clip.

Part of the Video Series: Radical Numbers
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Video Transcript

Hey there, it's Dr. K. with "Infinite Magic Productions". In today's tutorial we're going to learn how to convert a decimal into a radical. So let's do some examples. Let's start off with a decimal such as 2.828. So you're required to turn this decimal into a radical. A radical is a function with a square root, a cubic root or some kind of root. So we know that a larger number, when you take the square root, the cubic root or a higher root of it, is going to equal 2.828 but we don't know what. So the simplest way to do this is going to be keep multiplying this number by itself until you reach a whole number. So if we take 2.828 and multiply it by itself so it's 2.828 squared, you're going to get an approximate number of 7.9... So from here you know that because 2.828 isn't an exact number and when you square it you get 7.9939 for example, this means that 2.828 is derived from the square root of 8. It's a very rough approximation. So in this case we got lucky because we had a square root. So it was the square root of 8 that was equal to 2.828. Now let's say that we have a higher root but we don't know what it is. So let's say we're given 1.316 and we're supposed to convert this into a radical. So once again what we're going to start off with is taking 1.316 squared and this is going to come out to 1.73... So 1.73 isn't close enough to an even number such as 2 so we're going to keep multiplying it. So what we're going to figure out is that you need to take 1.73 squared again and in this case you get an approximation of 2.99... In this case 2.99 is close enough to 3 that we know that 1.316 had to be multiplied by itself four times in order to get 3. So the radical is 3 and it's a fourth root. Remember that in some cases you're going to get an index of 3, here for example this is the index in which case you would have to take the decimal that you're given and multiply it by itself three times and here in all these examples we used an even index so we had to multiply the number by itself several times or square it several times. In some cases you can try this at home if you take the third root of a number, so let's just do an example. We're going to take the third root of 7 and what you can do at home is take out your calculator, take the third root of 7, see what it's equal to, then take that number and multiply it by itself three times. In that case you get an approximation such as 6.98 or 6.99 where you know that your approximation is close enough to 7. So there you have it, that's how you convert decimals into radicals. Thanks for watching and come back for more. I'm Dr. K.

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