What Does X Mean In Math latest 2023

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

You can see more content about What Does X Mean In Math on our youtube channel: Click Here

Question about What Does X Mean In Math

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

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

Rate Articles What Does X Mean In Math

Rate: 4-5 stars
Ratings: 7781
Views: 67741213

Search keywords What Does X Mean In Math

What Does X Mean In Math
way What Does X Mean In Math
tutorial What Does X Mean In Math
What Does X Mean In Math free
#Pythagoras #Theorem #Irrational #Numbers

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

Related Posts

default-image-feature

What Does The Mean In Math latest 2023

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

default-image-feature

What Does R Mean In Math latest 2023

You are searching about What Does R Mean In Math, today we will share with you article about What Does R Mean In Math was compiled and…

default-image-feature

What Does Log Mean In Math latest 2023

You are searching about What Does Log Mean In Math, today we will share with you article about What Does Log Mean In Math was compiled and…

default-image-feature

What Does Differ Mean In Math latest 2023

You are searching about What Does Differ Mean In Math, today we will share with you article about What Does Differ Mean In Math was compiled and…

default-image-feature

What Does A Sum Mean In Math latest 2023

You are searching about What Does A Sum Mean In Math, today we will share with you article about What Does A Sum Mean In Math was…

default-image-feature

I Know It Math 3Rd Grade latest 2023

You are searching about I Know It Math 3Rd Grade, today we will share with you article about I Know It Math 3Rd Grade was compiled and…