Finding distance in three variable function

[sibellius]

Hello all,

I've been struggling with this problem for a little while and could use some help.

"Consider the plane 3x+6y+10z= 18001

What is the exact distance from the x-intercept to the y-intercept?"

If this was 3x+6y+10z=18000 there'd be no problem, but the fact that its odd is causing me some problems. So I've got the x and y intercepts are ((18001/3), 0 , 0) and (0, (18001/6), 0) respectively. Plugging them into the distance equation gives me

sqrroot (-18001/3)^2 + (18001/6)^2

From here (assuming I've done everything right so far) is where it gets tough for me. Would I add the two fractions (since they have like exponents)? The sqrroot would then cancel out the exponent, leaving me with -18001/6. It seems that the problem is not allowing for the answer to be a decimal approximation. Is there a way to simplify the fraction?

 

[galactus]

\(\displaystyle \sqrt{\left(\frac{18001}{3}\right)^{2}+\left(\frac{18001}{6}\right)^{2}}=\sqrt{\frac{1620180005}{36}}=\frac{\sqrt{90005\cdot 18001}}{6}=\frac{\sqrt{5\cdot 18001\cdot 18001}}{6}=\frac{\sqrt{5\cdot 18001^{2}}}{6}=\)

\(\displaystyle \frac{18001\sqrt{5}}{6}\approx 6708.58\)