find rational number r=m/n . Such that √5 < r < √6
The distance between the numbers and is equal to
Therefore, if , then the length of the interval ( ) is equal to and this interval must contain an integer m.
We have and, therefore, the ratio m/n belongs to the interval .
To find the ratio m/n in the interval we should seek a full-squared integer m2 in the interval (5n2, 6n2).
Let's take n=5.
The only full-squared integer between 125 and 150 is 144=122=m2.
Therefore, r=m/n = 12/5 = 2.4 satisfies the original condition.
Comments