# Video: Identifying the Position of Irrational Numbers on a Number Line

Identify which of the arrows represents the position of √90.

02:27

### Video Transcript

Identify which of the arrows represents the position of root 90.

So the first thing we need to think about is what does root 90 mean? Well, root 90 means that there is a number I’m gonna call 𝑛. And this number if you square it is gonna be equal to 90. Well, how could we determine what this number is going to be or at least where this number will lie on our number line? Well, what we can do to help us is list our square numbers.

So what we’re gonna think about is the first 10 square numbers. So we got one squared, which is one, two squared is four, three squared is nine, four squared is 16, then 25, 36, 49, 64, 81, and finally, 10 squared is equal to 100. So why have I stopped at 10 squared or 100? Well, we stopped there because 100 is greater than 90. And we’re interested in the square root of 90. So what number squared gives us 90?

Well, first of all, if we take a look at a, we can see that a is between three and four. So therefore, if we square three and four, we get nine or 16. So Therefore, we’d expect the number within the square root to be between nine and 16. Well, 90 clearly isn’t because it’s much bigger than these values. So therefore, we can rule out a. Well, next, we can move on to b. Well, b is between five and six. Well, that means if we square five and square six, we get 25 and 36, respectively. Well, 90 is not between these two values. So we can rule out b.

So then, if we look at between seven and eight, which is c, we’ve got 49 and 64 because seven squared is 49 and eight squared is 64. Again, 90 is not between these two values. So we can rule out c. So therefore, we’re gonna expect that d is the correct answer. Well, d is between nine and 10. And if we check this out, well, nine squared is 81 and 10 squared is 100. Well, 90 is between 81 and 100. So therefore, we can say that root 90 is gonna be between nine and 10.

So therefore, we can say that the correct arrow that represents the position of root 90 is gonna be arrow d.