Find the length of the missing side of this right triangle.

You want to use the pythagorean theorem here.
a^2 + b^2 = c^2, where a and b are side lengths and c is the hypotenuse.

you're given your hypotenuse -- 6 inches -- and one side -- √3 inches. plug these into your formula:

(√3)^2 + b^2 = 6^2 ... now simplify
3 + b^2 = 36 ... subtract 3
b^2 = 33 ... cancel out the exponent by taking the sq root of both sides
b = √33 inches is your missing length.