Question 72726
1) One advantage is when multiplying.  For example:
{{{sqrt(3)*[3]sqrt(3)}}} This is easier to understand when written this way: {{{3^(1/2) * 3^(1/2) = 3^(((1/2)+(1/2)))}}} = {{{3^1 = 3}}}

2) For this problem, use the Pythagorean theorem: {{{c^2 = a^2+b^2}}}
a=35 km and b = 65 km.  Let d = the unknown distance.
{{{d^2 = 35^2+65^2}}} Simplify.
{{{d^2 = 1225+4225}}} 
{{{d^2 = 5450}}} Take the square root of both sides.
{{{d = sqrt(5450)}}}
{{{d = 73.824}}}
{{{d = 73.8}}}km. (Rounded to the nearest tenth)

3) {{{V = s^3}}} To find s, take the cube root of both sides.
{{{729 = s^3}}} Take the cube root.
{{{9 = s}}} The length of the side is 9 cm.