The answer, the simplified radical and the working — so the next one you can do in your head
Type any number to get its square root to four decimal places, the exact simplified form, the two perfect squares it sits between and the estimate you can make without a calculator. The working matters more than the answer: once you can see that √60 sits between √49 and √64, closer to 64, you can place any root in a second.
About 7.746. In exact form it is 2√15, because 60 = 4 × 15 and √4 = 2. It sits between 7 (√49) and 8 (√64).
Find the largest perfect square that divides the number, take its root outside the radical and leave the rest inside. √72 = √(36 × 2) = 6√2.
Find the perfect squares either side, then place the number between them by distance. √40: between 36 and 49, 4 of the 13 steps up, so about 6.3. The true value is 6.32.
Not as a real number — no real number times itself is negative. In complex numbers √−9 = 3i, but this calculator works with real numbers only.
Yes. 13 × 13 = 169, so 169 is a perfect square and its root is a whole number. That is also why 169 ÷ 13 = 13.