find tow irrational number between 786 and 787
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Irrational numbers are not very special. I don’t know why people on Quora seem to be so interested in them. They are just real numbers that aren’t rational. At least rational numbers are closed — add, subtract, multiply, or divide two rational numbers, and you get a rational number. But you aren’t guaranteed that adding, subtracting, multiplying or dividing two irrational numbers will give you an irrational number.
Here’s a thing that’ll help: For any rational number pqpq, with gcd(p,q)=1,gcd(p,q)=1, the square root pq−−√pq is rational if and only if both ppand qq are perfect squares (i.e., there are integers a,ba,b such that a2=p,b2=pa2=p,b2=p.
Here’s a thing that’ll help: For any rational number pqpq, with gcd(p,q)=1,gcd(p,q)=1, the square root pq−−√pq is rational if and only if both ppand qq are perfect squares (i.e., there are integers a,ba,b such that a2=p,b2=pa2=p,b2=p.
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