Question

Find tua irrational numbers between
0.7 and 0.77​

Answer 1

Answer:

If p,qp,q are two rational numbers (p<q),(p<q), then an irrational number in the range [p,q][p,q] is, pp+q−p2√+q−p2. And using this trick you can make infinite number of irretional numbers within range [p,q][p,q]. You just need to keep adding a real part which keeps the number, n<qn<q.

For example, in your case p=0.7,q=0.77p=0.7,q=0.77

0.7+0.77−0.72√=0.7130...0.7+0.77−0.72=0.7130...

Couple of next irrational numbers:

0.1+0.7+0.77−0.72√=0.7230...0.1+0.7+0.77−0.72=0.7230...

0.2+0.7+0.77−0.72√=0.7330...0.2+0.7+0.77−0.72=0.7330...

0.3+0.7+0.77−0.72√=0.7430...0.3+0.7+0.77−0.72=0.7430...

0.4+0.7+0.77−0.72√=0.7530...0.4+0.7+0.77−0.72=0.7530...

0.5+0.7+0.77−0.72√=0.7630...0.5+0.7+0.77−0.72=0.7630...

Stop here before 0.7730… because it will cross 0.77 ( q )

At that moment if you want more irrational numbers between, you can rather add something like,

0.001,0.002,…,∞0.001,0.002,…,∞

Answer 2

Answer:

Irrational numbers are 0.71010010001.....

0.72020020002....