The value of $\sqrt{203}$ is between the two consecutive whole numbers and

Step 1 ：The square root of a number is the value that, when multiplied by itself, gives the original number. To find the two consecutive whole numbers that the square root of 203 is between, we need to find the square root of 203 and then determine the two whole numbers that this value falls between.

Step 2 ：Calculate the square root of 203: \(\sqrt{203} \approx 14.25\)

Step 3 ：The square root of 203 is approximately 14.25. This means that it falls between the whole numbers 14 and 15.

Step 4 ：Final Answer: \(\boxed{The value of \sqrt{203} is between the two consecutive whole numbers 14 and 15.}\)