TI-84 Plus CE and TI-Nspire CX II: Square Root Trick - by @Mathsbook7474
From the Instagram account @Mathsbook7474, it is stated that the square root of a number can be approximated by:
√x ≈ (x + y) ÷ (2 · √y)
where y is the number nearest to the root, preferably a perfect square. (see source for the link)
Let x = 52. Note that 49 is a perfect square near to 52. Since √49 = 7, let y = 49.
√52 ≈ (52 + 49) ÷ (2 · √49) = 7.214285714
Accuracy: 0.0031831631 (√52 = 7.211102551)
TI-84 Plus CE Program: SQAPPROX
The program SQAPPROX will calculate the approximation above, the actual root, and compare the results for the accuracy.