How to find number between two irrational numbers

1.	How to find number between two irrational numbers
Answer» This is just an example Let us convert 5/7 and 9/11 into decimal form, to get\xa05/7 = 0.714285... and 9/1 = 0.818181.... .Three irrational numbers that lie between 0.714285.... and 0.818181.... are:0.73073007300073….0.74074007400074….0.76076007600076…. Suppose we have two rational numbers a and b, then the irrational numbers between those two will be,\xa0√ab. Now let us find two irrational numbers between two given rational numbers.1. Find an irrational number between two rational numbers 2 –\xa0√3 and 5 –\xa0√3Let x be the irrational number between two rational numbers 2 –\xa0√3 and 5 –\xa0√3. Then we get,2 –\xa0√3\xa0< x\xa0< 5 –\xa0√3⇒\xa02 < x + < √3\xa0< 5We see that x + √3 is an irrational number between\xa02 –\xa0√3 and 5 –\xa0√3 where 2 –\xa0√3\xa0< x\xa0< 5 –\xa0√3.2. Find two irrational numbers between two given rational numbers.Now let us take any two numbers,\xa0say a and b. Let x be any number between a and b. Then,We have a\xa0< x\xa0< b….. let this be equation\xa0(1)Now, subtract\xa0√2 from both the sides of equation\xa0(1)So, a –\xa0√2\xa0< x\xa0< b –\xa0√2……equation (2)= a < x +\xa0√2 < bAddition of irrational number with any number results into an irrational number. So, x +\xa0√2 is an irrational number which exists\xa0between two rational numbers a and b.

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