The Pythagorean theorem states the relationship between a right triangle's legs and its hypotenuse: if the legs' lengths are a and b and the hypotenuse's length is c, then a2 + b2 = c2.
In your question, we have a right triangle with one leg 4 inches long, the other leg an unknown x inches long, and the hypotenuse √23 inches long, Substituting these into the formula, we get: 42 + x2 = (√23)2.
42 = 16, and (√23)2 is just 23, so if you substitute these values in and subtract 16 from both sides, you get x2 = 23 - 16 = 7.
Taking the square root of both sides, we get x = √7. So our final answer is, the exact length of the other leg is √7 inches.