x is an irrational number between 7 and 10. find a value for x

=2.915475947422650235437076438772791538260699167442985977225003372433905030998356313832620163226517699278394811037677455675906936808085403142951613039412223590832527179885119634084324188271634828210865

The shown decimal goes on for 200 digits.

And it cannot be put into fraction form, meaning it is irrational.

Hope this help :)

MrRoyal MrRoyal · Answer 2 · 2021-08-14T00:12:52+02:00

Literally, irrational numbers are numbers that cannot be expressed as simple fractions. Some irrational numbers between 7 and 10 are 7.4833,7.9372,8.3666,8.4852,9.4868.

Given that

[tex]Min = 7[/tex]

[tex]Max = 10[/tex]

There are several ways to generate the irrational numbers between the given range.

One of the ways is as follows:

First, we list the pairs of relatively prime integers between the given range.

They are:

[tex]x = \{(7,8),(7,9),(7,10),(8,9),(9,10)\}[/tex]

Calculate the product

[tex]x = \{56,63,70,72,90\}[/tex]

Take the positive square root of the numbers to generate some irrational integers

[tex]x = \{\sqrt{56},\sqrt{63},\sqrt{70},\sqrt{72},\sqrt{90}\}[/tex]

[tex]x = \{7.4833...,7.9372....,8.3666...,8.4852....,9.4868....\}[/tex]