Question 371971
{{{3sqrt(1000)}}}
Simplify does not mean find a decimal approximation. Simplifying an expression with a square root means reduce the square root, if possible. Reducing a square root is done by finding perfect square factors, if any, of the radicand (the expression within the radical). So we are looking for perfect square factors of 1000. I hope it is easy to see that 100 is a perfect square and it is a factor of 1000:
{{{3sqrt(100*10)}}}
Next we use a property of radicals, {{{root(a, p*q) = root(a, p) * root(a, q)}}}, to separate the perfect square factor into its own square root:
{{{3sqrt(100)*sqrt(10)}}}
The square root of 100 is 10 so now we have:
{{{3*10*sqrt(10)}}}
or
{{{30sqrt(10)}}}
There are no other perfect square factors of 10 (other than 1) so this simplified version of {{{3sqrt(1000)}}}. (BTW, the decimal approximation for this is 94.8683298050513800)