Answer:
We want to find two irrational numbers between 0.8275496 and 0.84218972
The easier way to solve this is to remember that the product between an irrational number and a rational number (different than zero) is irrational. Then:
Now, remember that the square root of a prime number is always irrational, so we can start working with that.
√5 = 2.236......
As our two rational numbers are 0.8275496 and 0.84218972, any irrational number such that the first two digits after the decimal point are 0.83 will be between these, then we can do the calculations with rational numbers:
2.236 and 0.83
2.236*A = 0.83....
Where A is a rational number:
A = 0.83/2.236 = 0.371
Now we know that 0.371 is a rational number, then:
0.371*√5 will be an irrational number, and:
0.371*√5 = 0.82958....
then 0.371*√5 is an irrational number between 0.8275496 and 0.84218972
Now let's find other, this time using √2.
√2 = 1.414....
1.414*A = 0.83
A = 0.83/1.414 = 0.587
Then:
0.587*√2 will be an irrational number, and:
0.587*√2 = 0.830143...
So 0.587*√2 is an irrational number between 0.8275496 and 0.84218972
