Final answer:
The square root of 346 is a value between 18 and 19, and it is approximately 18.601. To determine this without a calculator, estimation methods such as the babylonian method are used.
Step-by-step explanation:
The square root of a number is a value that, when multiplied by itself, gives the original number. Calculating the square root of 346 can be approached by estimation since 346 is not a perfect square. To find the square root of 346, we know that 18 squared is 324 and 19 squared is 361. Therefore, the square root of 346 is between 18 and 19. Using a calculator, we can find that it is approximately 18.601. However, without a calculator, we would rely on methods such as the babylonian method or other estimating techniques to narrow down the value as closely as possible.