A worked example: the diagonal of a 15 × 20 rectangle
A rectangular plot measures 15 units by 20 units and you need the length of its diagonal. The basic math calculator handles the first three steps, one operation at a time: multiply 15 by 15 to get 225, multiply 20 by 20 to get 400, then add 225 and 400 to get 625. That last number, 625, is the sum of the squares — but the basic math calculator's operation list stops at add, subtract, multiply, and divide, so it cannot take the square root needed to finish. Feeding 625 into the scientific calculator as sqrt(625) returns 25, the exact length of the diagonal.
The formula: three basic operations feeding one scientific function
The Pythagorean theorem states that for a right triangle with legs a and b, the hypotenuse c satisfies c = sqrt(a² + b²). Squaring a and b, and adding the results, are each single arithmetic operations — exactly what the basic math calculator's operation field supports one at a time. The square root, however, is not one of that calculator's four options; it belongs to the function set (sqrt, sin, cos, tan, log, ln, abs) that only the scientific calculator's expression evaluator understands. So the real result of one calculator, 625, becomes the real input to the other, entered directly as sqrt(625).
A worked example: the diagonal of a 9 × 40 rectangle
The same chain scales to different numbers. For legs of 9 and 40: multiply 9 by 9 on the basic math calculator to get 81, multiply 40 by 40 to get 1600, then add 81 and 1600 to get 1681. Entering sqrt(1681) into the scientific calculator returns 41 — again a whole number, because 9-40-41 is a Pythagorean triple just as 15-20-25 is, but the chain would work identically for legs that don't produce a clean integer, simply returning a decimal like the scientific calculator's sqrt(2) result of 1.4142135623730951 instead.
Why splitting the calculation across two calculators makes sense
The basic math calculator and the scientific calculator are not competing tools — they cover different halves of the same class of problem. Squaring and adding are exact, single-operation steps well suited to a calculator that does one operation at a time and shows its rounding rules plainly; the square root is a function that only the expression evaluator's broader operation set supports. Recognizing which half of a multi-step calculation each calculator is built for — plain arithmetic versus functions and operator precedence — is what makes a real calculation like a rectangle's diagonal solvable in two deliberate steps instead of needing a single do-everything tool.