Question 343532
{{{7sqrt(32)/9sqrt(8)}}}
As is often the case in Math, there is more than one way to simplify this expression. To me the easiest way is based on noticing that dividing 32 and 8 (which are currently inside separate square roots) results in 4 which is a prefect square!<br>
So we will start by getting the 32 and the 8 into the same square root. First we'll use basic Algebra to split this fraction in two:
{{{(7/9)*(sqrt(32)/sqrt(8))}}}
Now we can use one of the properties of radicals:
{{{sqrt(a)/sqrt(b) = sqrt(a/b)}}}
to combine the square roots of the second fraction into a single square root:
{{{(7/9)*sqrt(32/8)}}}
Now we can replace the 32/8 with a 4:
{{{(7/9)*sqrt(4)}}}
and the {{{sqrt(4)}}} with a 2:
{{{(7/9)*2}}}
And we finish by multiplying:
{{{14/9}}}
(I'll leave it up to you to change this improper fraction into a mixed number.)