Question 226003
{{{sqrt(49)/sqrt(4)}}}
You can look at these 2 radicals separately
{{{sqrt(49) = 7}}} and
{{{sqrt(4) = 2}}}, so
{{{sqrt(49)/sqrt(4) = 7/2}}}
but, also
{{{sqrt(49)/sqrt(4) = sqrt(49/4)}}}
{{{sqrt(49/4) = sqrt(12.25)}}}
On my calculator, 
{{{sqrt(12.25) = 3.5}}}
{{{3.5 = 7/2}}}
So, both ways of solving are equivilant
also
{{{(sqrt(10)*sqrt(16))/sqrt(5)}}}
{{{sqrt(10) = 3.1623}}}
{{{sqrt(16) = 4}}}
{{{sqrt(5) = 2.2361}}}
so,
{{{(sqrt(10)*sqrt(16))/sqrt(5) = (3.1623*4)/2.2361}}}
{{{(3.1623*4)/2.2361 = 12.6492/2.2361}}}
{{{12.6492/2.2361 = 5.6568}}}
but, simplifying,
{{{(sqrt(10)*sqrt(16))/sqrt(5) = sqrt(10*16)/sqrt(5)}}}
{{{sqrt(10*16)/sqrt(5) = sqrt((10*16)/5)}}}
{{{sqrt((10*16)/5) = sqrt(32)}}}
{{{sqrt(32) = sqrt(16*2)}}}
{{{sqrt(16*2) = sqrt(16)*sqrt(2)}}}
{{{sqrt(16)*sqrt(2) = 4*sqrt(2)}}}
Now, I'll see if I get the same answer before I simplified
{{{4*sqrt(2) = 4*1.4142}}}
{{{4*1.4142 = 5.6568}}}
Both methods give the same answer
I hope this helps