SOLUTION: Write 3 irrational numbers between 3/5 and 4/5

Algebra ->  Real-numbers -> SOLUTION: Write 3 irrational numbers between 3/5 and 4/5      Log On


   

Question 1013465: Write 3 irrational numbers between 3/5 and 4/5
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Since %283%2F5%29%284%2F5%29 is not a perfect square,
sqrt%28%283%2F5%29%284%2F5%29%29 is an irrational number between 3/5 and 4/5.
.
sqrt%28%283%2F5%29%284%2F5%29%29%29=sqrt%2812%2F25%29=sqrt%2812%29%2F5=2sqrt%283%29%2F5
ANSWER 1: First irrational number between 3/5 and 4/5 is 2sqrt%283%29%2F5
.
Since %283%2F5%29%282sqrt%283%29%2F5%29 is not a perfect square,
sqrt%28%283%2F5%29%282sqrt%283%29%2F5%29%29 is an irrational number between 3/5 and 2sqrt%283%29%2F5.
.
sqrt%28%283%2F5%29%282sqrt%283%29%2F5%29%29=sqrt%286sqrt%283%29%2F25%29=sqrt%286sqrt%283%29%29%2F5
ANSWER 2: A second irrational number between 3/5 and 4/5 is sqrt%286sqrt%283%29%29%2F5
.
Since %284%2F5%29%282sqrt%283%29%2F5%29 is not a perfect square,
sqrt%28%284%2F5%29%282sqrt%283%29%2F5%29%29 is an irrational number between 4/5 and 2sqrt%283%29%2F5.
.
sqrt%28%284%2F5%29%282sqrt%283%29%2F5%29%29=sqrt%288sqrt%283%29%2F25%29=sqrt%288sqrt%283%29%29%2F5
ANSWER 2: A third irrational number between 3/5 and 4/5 is sqrt%288sqrt%283%29%29%2F5=+2%28sqrt%282sqrt%283%29%29%29%2F5
.