Harvard University Simplification Tricks | Radical Algebra Aptitude Test | Ivy League Entrance Exam

Published: Aug 27, 2024 Duration: 00:10:32 Category: Education

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hello and welcome how to simplify this radical expression the square root of 993 into 995 into 997 into 999 + 16 calculators are not allowed now solution let us have the mean of these factors so before we have the mean let us change the form of these factors so let us change the forms of the factors and have the mean so we have 1,000 - 7 is the same as 993 plus 1,00 - 5 + because 1, - 5 you get this now next 1,000 - 3 you get this so we have 1,00 - 3 + 1, - one to obtain that so all over this how many factors do we have 1 2 3 4id by 4 so this is the mean we are looking for now 1,000 + 1,000 + + 1,000 + 1,000 = to 4,000 so next this one equals to 4,000 - 7 - 5 - 3 - 1 = to - 16 so - 16 of this over four now this one gives us by isolating the individual fractions so we have 4,000 4 16 / 4 this one F gives us so this one becomes 1,000 so we have 1,000 so this one becomes 4 - 4 so which means that mean equals to mean of the factors = to 1, - 4 = to 996 now we have the mean now let now here let X Beal to 996 now let us change let us express the all of this factors in terms of 996 we said that X = to 9 96 so we have let X to be 996 now let us express all these factors in terms of 996 so we have therefore x - 3 = to 9 93 x - 1 = to 9 95 x + 1 = 9 97 x + 3 = to 999 so you can see now we have expressed all these factors in terms of the average so let us put in this new forms so next we have next we have x - 3 into X - 1 into x + 1 into into x + 3 + 16 then you apply the square root of the all of this expression now this one is this one equals to now this one becomes by rearranging bring this one and this one together and the Met terms together so let us have the product of the metal factors and the product of the rest two factors so so we have x - 3 into x + 3 into X - 1 into x + 1 + 16 you apply the square root to maintain the meaning of the expression so the first two forms the differ of two squares and the last two factors form the difference of two squares so this one equals to theare root of x 2 - 3 2 into x 2 - 1 2 + 16 now this one f equals to the sare root of we have x^ 2 - 9 is9 into X2 - 1 + 16 now let us expand F this one here so here we have the square root of x^2 into x^2 - 1 - 9 into x² - 1 + 16 now this one equals to now this one here gives us the square root of x 2 * x 2 so we have x^ 4 - x 2us now here we have 9 x² + 9 + 16 so by simplifying Factor this one gives us x^ 4 the root of x to^ 4 here we have - 10 x 2 99 + 16 you get 25 so we put 25 here x to^ 4 - 10 x 2 + 25 forms a complete Square so express it as a perfect square so this one is the same as the square root of x 2 of this s - 2 * 5 x 2 + 5 S so you can see this is a complete Square now by the application of this rule that a 2 - 2 a p+ p s is the same as a minus P squ so we going to use this identity to simplify this so next now by the application of the identity that a 2 - 2 a p + p s = to a minus P of D squ Now by changing this form into to this here therefore this one becomes x 2 minus 5 squ then you apply the square root so as you can see this one cancels with this now next this one becomes X2 - 5 but X = to 996 so here we have 9 96 2 - 5 so this one going to be written as X = to 1,00 - 4 so next this one is the same as 1,00 - 4 of this squ - 5 now let us apply this identity once again here so this one becomes 1,00 2 - 2 * 1,00 * 4 + 4 2 - 5 so this one becomes so this one is the same as 1 million so we have 1 million here so this one becomes 8,000 - 8,000 + 16 - 5 now here if we subtract 8,000 from this we have if we start with so here we have 9 9 2 0 0 0 plus 16 - 5 get 11 so this one gives us 9 9 2 0 11 11 now you can see we have obtained the solution without using calculators which you mean that the square root of 993 into 995 into 997 into 999 + 16 equal to 99 2 011 and that is it thank you for watching subscribe to my channel and turn on the notification Bell get new updates when I upload videos don't forget to smash like button share and comment below to make this video many people

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