Question

14 (OM) Radicals and Estimation (2 pts) Without a calculator, estimate the radical and explain how you estimated. Then using a calculator and compare your estimation and the approximation.Example:(1 + 2sqrt(5))/4Estimate without a calculator: boxed 1,3Explanation: I estimate (l + 2sqrt(5))/4 to be approximately 1.3, because...√5 is between sqrt(4) and sqrt(9) , but closer to sqrt(4) (since 5 is closer to 4 than it is to 9). Since sqrt(4) is 2. sqrt(5) is probably something like 2.1 or 2.2. Filling 2.1, In the expression and simplifying, we have this:l+2^ * 2.1 4 = 1+4.2 4 = 5.2 4 =1.3 So, I expect the number (2sqrt(5) + 1)/4 to be close to 1.3. [Note: The goal here is NOT to be exact! This problem will be graded on explanations of your reasoning.]a)NO CALCULATOR(1; ) 3 - sqrt(38)Estimate without a calculatorExplanation:b) CALCULATOR ALLOWED (1 pt) For the same problem given in part " a^ * above, use a calculator toapproximate, rounding to the hundredths. Use correct notation for approximation. Compare your estimation and the approximation. Does your estimation seem to be correct? Why or why not?

Answer 1

Q) Without a calculator, we must estimate the value of the following expression:

$3-\sqrt[]{38}.$

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:

$3-6.2=-3.2.$

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.