Question 729894
{{{6root(4,8)+7/root(4,2)}}} has a root in the denominator and we do not like roots in denominators.
 
To get rid of the root in the denominator of {{{7/root(4,2)}}} we multiply numerator and denominator times {{{root(4,8)}}} .
We choose that because
{{{2*8=16=2^4}}} <--> {{{root(4,2)root(4,8)=root(4,2*8)=root(4,16)=root(4,2^4)=2}}}
 
{{{6root(4,8)+7/root(4,2)=6root(4,8)+7root(4,8)/root(4,2)/root(4,8)=
6root(4,8)+7root(4,8)/root(4,2*8)=
6root(4,8)+7root(4,8)/root(4,16)=6root(4,8)+7root(4,8)/2=
6root(4,8)+(7/2)root(4,8)=(6+7/2)root(4,8)=highlight((19/2)root(4,8)=19root(4,8)/2)}}}
 
NOTE: I showed each baby step in the solution.
If you have to "show your work" you may want to skip some steps.
Only you can decide what is so obvious that should be skipped.
That is always a gamble, because you may skip steps that may seem obvious to you, but if your teacher does not think they would be so obvious to you, you may be accused of copying parts of someone else's solution.