Why do even the simplest calculators feature a square root key?

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In modern times, a basic electronic calculator is a piece of dollar store trash that the tech-illiterate use to balance their checkbook, but in the 1960s they were serious business. Early adopters of calculators included scientists and engineers, which had come to expect a square root function from their slide rules. While implementing square (and cube) roots on a slide rule is extremely simple, it was quite complicated to do it with discrete diodes and transistors. In the late 1960s, the inclusion of a square root function represented a cost increase measured in hundreds of dollars. The square root function became associated with advanced and costly scientific functionality before true scientific calculators became prolific.

To give you some actual numbers, the earliest machine I have which includes a square root function is a Busicom 162. It was manufactured in 1967, and retailed for 298,000 yen, or about $830 in 1967 dollars (the yen/dollar exchange rate was fixed at 360:1 throughout the 1960s). The price difference between the 162 and the root-less model 162C was 38,000 yen or $105, approximately a $500 price difference when adjusted for inflation.

When the price of hardware imploded in the early 1970s, square root was implemented in some commodity calculator chips from companies like TI and Mostek, and often became a differentiator between high and low end four-bangers in the same series. Companies would offer multiple iterations of the same machine, with and without a square root function. Casio in particular was fond of including it right in the calculator's model name, with models like the ROOT-121A (which actually used the square root symbol in its model name) and ROOT-8S. By this point, the cost of square root was measured in tens of dollars. The majority of four-bangers still did not have a square root function, and the inclusion of square root was still a marketable feature, even as true scientific calculators were transitioning from the HP-35 price point to the TI-30 price point in the mid-70s.

By the early 1980s, square root had become a value-added feature with a negligible production cost increase, and was simply included to avoid losing a sale to another calculator with square root. Forty years later, they have become a tradition.