Q) Without a calculator, we must estimate the value of the following expression:
A) I estimate 3 - √38 to be approximately -3.2.
First, we estimate the value of √38. √38 is between √36 and √49, but close to √36 (since 38 is closer to 4 than it is to 9). Since √36 is 6, √38 is probably something like 6.1 or 6.2. Filling 6.2 in the expression and simplifying, we have this:
So, I expect the number 3 - √38 to be close to -3.2.
Using a calculator we find that: 3 - √38 ≅ -3.16, which it is approximately the result that we found.
Answer
Without a calculator we find that 3 - √38 ≅ -3.2.