# Practice English Speaking&Listening with: How to Plot Irrational Numbers on the Number Line Part 1 [with English subtitles]

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Hi guys, welcome to Sipnayan.

In this video, I will teach you how to plot

irrational numbers on the number line.

The irrational numbers that we are going to plot are

numbers of the form square root of n

where n is not a perfect square.

Let's read the instruction.

So you can try, you can pause the video

if you want to try on your own then we'll check you answers later.

I hope you paused and try to plot the points.

The easiest way we can do is to express

the numbers on the number line

of the form square root of n, right?

For example, 1 is square root of 1...

then 2 is square root of 4...

3 is square root of 9, and so on.

So for 9, we have square root of 81,

and 10 is square root of 100.

By expressing the numbers as square root of n

it's easier to locate the given

although it's just an estimate, because we can't really locate

unless we have a calculator,

and even if we have a calculator, it will still be an estimate.

Okay, where do you think is square root of 7?

But most likely, it's closer to square root of 9, right?

Because square root of 7, square root of 8,

square root of 9...it's closer here [to 9], right?

So most likely square root of 7 is here.

Again, we just estimate.

Somewhere here, but...

it's closer to square root of 16 because

square root of 16, square root of 17 then square root of 18,

square root of 25 is a bit farther, so it's somewhere here

It's the same with square root of 23,

it's a little bit closer to square root of 25.

square root of 24 then square root of 25.

So it looks like it's here.

30 is close to...

is it closer to 25 or 36?

Looks like it's a little bit closer to 25,

so it seems like it's close to the middle.

By the way, it's not linear,

the distance between square root of 26

minus square root of 25 is not equal to the

square root of 25 minus square root of 24,

it's not like that because it's not linear...

the distance between the two numbers with square root.

So we just rely on the estimation here.

it's close to the square root of 64, somewhere here...

then square root of 83, somewhere here...

it's very close to the square root of 81

and the square root of 90 is a bit close to the middle,

80 and 100 are a bit close to the middle,

so this is square root of 90.

Let's see. Using a calculator, let's see if our estimates are correct.

Okay, let's check square root of 7.

it's like close to 2 and 65 hundredths,

so 2 and 6 tenths, we can look at our estimate...

so are we close?

It's somewhere here, right? 2 and 6 tenths.

So we're not that far.

4 and 2 tenths, so let's check.

4 and 2 tenths, we're close... this ones a bit closer.

So 4 and 2 tenths, looks like we're right.

Next is square root of 23...

That's almost 4 and 8 tenths,

so 4 and 8 tenths, this is it.

So we're right.

So the square root of 30 is...

almost 5 and 5 tenths... it's almost 5 and 1 half,

very very close to 5 and 1 half.

Okay, so almost correct, right?

Almost 5 and 1/2.

So 7 and 8 tenths, we're almost correct here.

The square root of 83 is equal to...

So it's very very close to 9...

So almost the same, we're almost correct, 9 and 1 tenth.

The square root of 90 is equal to...

almost 9 and 5 tenths, almost 9 and 1 half,

it's in between 9 and 10.

So it's almost in the middle, this is it.

So what we missed is just this.

Okay so I didn't practiced that, as you can see we missed a bit,

but I want to show you that

it can be estimated although it can't be perfected

but we can get many right answers.

Okay, thanks a lot.

I hope you enjoyed this video.

Don't forget to subscribe, I'll see you in the next video.

The Description of How to Plot Irrational Numbers on the Number Line Part 1 [with English subtitles]