so class we are going to have a short exercise which is a continuation on our whole numbers working with the properties of whole numbers remember I was referring to the rational numbers in our previous class talking of the rational numbers the irrational just to know all the basics of your numbers so in this exercise you given between which two consecutive integers all right so guys when you're referring to something like consecutive that is in a certain order that you follow you're following a certain order one 2 3 4 five 6 these are consecutive terms so consecu like following each other like that so in this case they talking of consecutive integer that's we writing like two three following a certain pattern all right but in this case it is not of a pattern that you're going to follow now we are just talking about in between like two integers to say we've got another one then another integer there so they are saying between which two consecutive integers do the following irrational numbers likee already they have told you that these are irrational numbers they have already told you that they are irrational numbers remember irrational numbers those are the numbers that we cannot actually simplify by head the calculator can simplify it but us we cannot simplify by head these are endless decimal none nonterminating non recuring decimals so there saying square root of 11 where are we going to have the square root of 11 in between which numbers so meaning to say if it is in between certain numbers meaning to say it is supposed to be in between two values the square root of a number 11 can be greater than a value which is here or the square root of 11 is supposed to be what smaller than a value supposed to be here so we need a value here we also need a value here those are consecutive integers but these numbers are supposed to be what integers Tech note so how can you not that guys how can you not that one if you do not understand just simplify theare Ro of 11 guys just simplify it what is the square of 11 all right let's go to our calculator easier like that all right let's see our calculator the square root of 11 like this it is 3 comma look at this number 3A 3 1 16 like that it is something like that 3A 3 uh 1 six something like that 166 like that this is the number that we have so let's say I do not understand this square root concept I just know okay 3A 36 on my number line is like this there is a number which is called three here all right then moving from three going to the right side I'm going to have 3 1 3 2 whatever that I have so meaning to say this decimal that we talking about here which is the 3 3 1 66 like that which is the square root of 11 it is after this number three it is after three this is where we have our three this number is big bigger than 3 it is after three then we move on after that 3A 5 3A 6 3 7 3A 8 3A 9 up to what up to four 5 6 7 so we just need the integers that are boundaries these are the boundaries of the square root of 11 which is 3A 3 166 so it is in between three and what it is in between three and four the square root of 11 is found in between three and what three and four so you can say it is greater than three the same square root of 11 it is less than four so meaning to say it is found in between three and what three and four that is what that is what it means there that is what it means so if you understand it that way you can simplify it from the calculator like that or there's another way so this is another way which is actually the one that they need you to have it you can have it this way the square root of 11 you just notice that since what what made this one to be an irrational number it is because we cannot simplify the number that is inside of the square root so which square roots that we are able to simplify we can simplify all the square roots of the perfect squares the perfect squares since we have a square root we have to think of what perfect squares we are talking of what 1 squar which is 1 2 squar which is four 3 squar which is 9 4 S which is 16 5 squ which is 2 and so on these are the perfect squares that we talking about so in this case you're simply going to ask yourself the number that we have is 11 so in between it is in between which perfect squares because the number is under the square root so you're supposed to ask yourself it is in between which perfect squares it is in between what 11 maybe it is somewh here as you can see it is in between 9 and what 9 and 16 n is a perfect square 16 is a perfect square so we saying the square root of 11 can be what it can be written as it is greater than theare root of 9 but less than theare root of 16 we are putting the square root because the number is also under the the square root but because these are perfect squares they can be simplified what is theare root of 9 it is three okay what is theare root of 11 this one you just right because it is the one that is you are comparing there or you can write the the decimal it is up to you what about the square Ro of 16 it is what a four so as we can see guys we still have the same answer just like the previous case so we simply saying the square root of 11 is greater than three but less than less than four so meaning to say it is in between three and what it is in between three and four these are the integers that we are going to find it in between so that's it guys they will just give you a certain in a certain number which is uh which cannot be simplified let's say the square root of seven you just need to figure out which numbers do we have so it is supposed to be greater than what less than what let's figure out seven between which numbers can we find seven in these perfect squares we can see that s is in between four and what four and 9 on our perfect squares that is where seven is it is in between four and 4 and 9 so you say theare root of s is greater than the square root of 4 which is the smaller number but less than the sare root of n these are the boundaries of our perfect squares which we can simplify the square root of four we know this one is two what about theare root of 9 we know this one is three that is why we have to choose the perfect squares because we know that the square root the square roots of the perfect squares gives us integers guys any perfect square that you think of its square root is an integer so meaning to say the square root of seven lies between two and three these are the integers where it is found they can give you any number sare root of 20 square root of whatever that you're given that's how you figure out it is in between what if you are given 15 15 is in between which numbers if you are given 19 19 is in between which numbers 19 we can find it in between 16 and what 16 and 25 these are the perfect squares so that's how you simply answer these questions all right so I just hope guys you do as many questions as you can all right let's figure out this one that has got a negative on Part B where you given the square root of uh the square root of1 so we already see this saw this one on the square root of 11 so this one is just a negative that we are given but we already we already saw that one we already saw it with what with a positive so if we say this one lies between the square root if we said the square root of 11 lies between three and four like this that is what we said here what about when it is now the square root I mean the minus root of 11 minus root of 11 guys it means the number is carrying a negative remember I said you cannot simplify the square root ofus 11 guys please do not confuse that square root ofus 11 this one the minus is is inside the square root this one it's inside it cannot be simplified this one but it is different from our question the minus is outside of the square root so it can be simplified because it's minus then you write the square root then 11 like this so this one can be simplified minus 3 comma whatever that you have it can be simplified so meaning to say if this is same Asus 3 3 1 66 whatever you have there it lies between which whole numbers which integers which integers are we going to say it is greater than minus 3 less than4 are we going to say that okay let's let's be realistic in terms of negative values remember negative values is like this uh let's say this is where we have a zero there we are going to count -1 - 2 - 3 - 4 and so on so if you notice -3 is here- 4 is here this is where we have our values then the minus 3A 3 which is the minor 11 this one it is not this side it is in between these numbers in between here that's where we have our minus 3 comma 3 6 whatever6 that we have there which is the minus 11 so as we can see the boundaries it is no longer in this format because of negative values minus 4 is the smaller value so we say minus square root of 11 that we see here is greater than minus 4 the smaller value is-4 the bigger value is what isus 3 be very very careful on this solution so it lies betweenus 4 and-3 the bigger value isus remember when you're talking of negative values - 4 - 3 - 2 -1 Z and so on the numbers that are closer to zero are the bigger values minus 2 is bigger than -4 -1 is bigger than -4 so please take note you're supposed to know this from your grade eight mathematics all right so that's it guys questions can be given like that so we saw that is going to be minus 4 to minus 3 then we given another part which is pi/ two uh this one there's no way guys we need to know the decimal what is the equivalent of that Pi / two so let's see on our calculator so that we can figure out the integers which are in between there all right uh that that is Pi / 2 this is pi but for you to have this Pi you have to use shift so it's shift then you press this so you've got pi over 2 like this as a decimal it is 1A 5707 something like that 1A 57 something like that so 1A 57 guys it is in between which integers there's no square root there guys there's no square root we just need the integers there in between what the this is your number line This is where we have one this is where we have two and so on so you will notice that 1A 57 whatever that you have it is in between somewhere there in between one and what in between one and two so it is going to be greater than one but less than two remember your boundaries the smaller number first the bigger number at the end so that is how you write these boundaries so it is in between or it is going to be found uh between one and two that is where it is that is where we have this number the integers in between that number will be one and two what about minus 3 Pi you need to simplify first minus 3 Pi okay let's just quickly take this one minus 3 Pi what is the value corresponding to minus 3 Pi use your calculator again so this is minus 3 then shift we press your Pi like that as a DE that's- 9 42 something like that so it's in between which decimal this is a negative remember just like what I explained in our previous question uh let's say this is where you have your numbers they are going this side so Min - 9 is here - 10 is here- 11- 12 and so on and so on so take note the numbers will be going there that side so meaning to say- 942 is a number in between here it is going to be somewhere there that is where 9 42 be somewhere there this minus 3 so it's in between which values - 10 and- 9 these are the integers so it is greater than- 10 greater than the smaller value is the one that you write first greater than - 10 but the same minus 3 Pi is supposed to be less than the bigger value that you're given which is what which is minus 99 so it is found in between -10 and 9 so this will be your solution all right so that is how these questions can be given as you just need to work as much questions as you can uh like I said do revisions guys revisions is the only way uh out uh in this term you need to understand the basics and work as much questions because there's a lot that you need to know but that lot can be minimized if you do a lot of revisions so that's it guys till we meet again