What is the simplest radical form of #sqrt(5) / sqrt(6)#?

1 Answer
Jul 29, 2015

Answer:

#sqrt(5)/sqrt(6)=sqrt(5/6)=sqrt(0.8333...)#

Explanation:

When dealing with positive numbers #p# and #q#, it's easy to prove that
#sqrt(p)*sqrt(q)=sqrt(p*q)#
#sqrt(p)/sqrt(q)=sqrt(p/q)#

For instance, the latter can be proven by squaring the left part:
#(sqrt(p)/sqrt(q))^2=[sqrt(p)*sqrt(p)]/[sqrt(q)*sqrt(q)]=p/q#
Therefore, by definition of a square root,
from
#p/q=(sqrt(p)/sqrt(q))^2#
follows
#sqrt(p/q)=sqrt(p)/sqrt(q)#

Using this, the expression above can be simplified as
#sqrt(5)/sqrt(6)=sqrt(5/6)=sqrt(0.8333...)#