What Are X And Y In Math latest 2023

You are searching about What Are X And Y In Math, today we will share with you article about What Are X And Y In Math was compiled and edited by our team from many sources on the internet. Hope this article on the topic What Are X And Y In Math is useful to you.

Pythagoras Theorem and Irrational Numbers

It is interesting how the Pythagorean theorem helps to identify the location of an irrational number on the number line. Consider a number x which is a rational number but not a perfect square. It follows that the square root of x must be irrational, that is, a nonterminal, nonrecurring decimal number. Now our interest is in determining where this is on the number line. To do this, consider a right-angled triangle whose base is (x-1)/2 and the hypotenuse is (x+1)/2. What would be the height of this right triangle, i.e. the other arm of the right triangle? Let’s assume it’s there. The Pythagorean theorem tells us that the sum of the squares of the arms of a right triangle is equal to the square of the hypotenuse. Thus, in the triangle that we have just considered, we can write:

[(x – 1)/2]^2 + y^2 = [(x + 1)/2]^2

Where y^2 = [(x + 1)/2]^2 – [(x – 1)/2]^2

= [(x^2 + 2x + 1) / 4] – [(x^2 – 2x + 1) / 4]

= [(x^2 + 2x + 1) – (x^2 – 2x + 1)] / 4

= [x^2 + 2x + 1 – x^2 + 2x – 1)] / 4

= 4x ​​/ 4

=x

i.e. y^2 = x ⟹ y = √x

This is exactly what we were looking for, the square root of x which is irrational. Now the length of the third arm of the triangle we have constructed can be marked on the number line using a compass.

So if you’re looking for the size of √x, here’s how we do it. Mark a point A. Mark B such that AB = x units. Label C such that BC = 1 unit. In other words, AC = x+1. Bisector AC. If D is the bisection point of AC, AD = DC = (x+1)/2. Now what would be the length of DB? Since DC = (x+1)/2 and BC = 1, DB = DC – BC = [(x+1)/2] – 1. Either (x+1-2)/2 or (x-1)/2.

Now let’s construct the triangle. Draw a line perpendicular to AC in B. From D, intersect the vertical line in E such that DE = AD. We now have a right triangle whose base is (x-1)/2 and the hypotenuse is (x+1)/2. Can you see what the measure of BE will be? Of course, as we showed above, it will be √x. You can now transfer this length of BE to the number line, using the compass.

Try to represent √5, √7, √11, √6.8 and √9.5 on the number line. Each of them should barely take a few minutes or less.

Video about What Are X And Y In Math

You can see more content about What Are X And Y In Math on our youtube channel: Click Here

Question about What Are X And Y In Math

If you have any questions about What Are X And Y In Math, please let us know, all your questions or suggestions will help us improve in the following articles!

The article What Are X And Y In Math was compiled by me and my team from many sources. If you find the article What Are X And Y In Math helpful to you, please support the team Like or Share!

Rate Articles What Are X And Y In Math

Rate: 4-5 stars
Ratings: 5871
Views: 98877456

Search keywords What Are X And Y In Math

What Are X And Y In Math
way What Are X And Y In Math
tutorial What Are X And Y In Math
What Are X And Y In Math free
#Pythagoras #Theorem #Irrational #Numbers

Source: https://ezinearticles.com/?Pythagoras-Theorem-and-Irrational-Numbers&id=10377146

Related Posts

default-image-feature

What Are Variables And Constants In Math latest 2023

You are searching about What Are Variables And Constants In Math, today we will share with you article about What Are Variables And Constants In Math was…

default-image-feature

What Are These Called In Math latest 2023

You are searching about What Are These Called In Math, today we will share with you article about What Are These Called In Math was compiled and…

default-image-feature

What Are The Types Of Properties In Math latest 2023

You are searching about What Are The Types Of Properties In Math, today we will share with you article about What Are The Types Of Properties In…

default-image-feature

What Are The Two Straight Lines In Math latest 2023

You are searching about What Are The Two Straight Lines In Math, today we will share with you article about What Are The Two Straight Lines In…

default-image-feature

What Are The Sequences In Math latest 2023

You are searching about What Are The Sequences In Math, today we will share with you article about What Are The Sequences In Math was compiled and…

default-image-feature

What Are The Rules Of Math latest 2023

You are searching about What Are The Rules Of Math, today we will share with you article about What Are The Rules Of Math was compiled and…