jmc

We use the distance formula: $$\sqrt{(7-0{)}^2+((-24)-0{)}^2}=\sqrt{49+576}=\sqrt{625}=\boxed{25}.$$- OR -

Note that the origin, the point $(7,-24)$, and the point $(7,0)$ form a right triangle with legs of length 7 and 24. This is a Pythagorean triple, so the length of the hypotenuse is $\boxed{25}$.