What is the difference between exact and estimated? Give an example using square roots.?

Answer 1

The area of a square is 3. What would be the dimensions of each side?

The exact value is √3 (because √3 x √3 = 3)

The estimated value is approximately 1.732. Note: irrational numbers like √3 can't be given with an exact decimal value, only an approximation because their decimal value goes forever without repeating.

Answer 2

The square of 9 is 3 exactly because 3 squared gives back 9.

The square root of 2 is 1.414 approximately to three places. The exact value goes on as a non-repeating decimal for ever. 1.414 is the approximate square root of 2 since squaring 1.414 gives a value slightly less than 2. No matter how many decimal places you use, squaring the value will never produce 2. But you can use enough decimal places to get an answer upon squaring as close to 2 as you wish.

The only exact value is sqrt(2) since squaring this gives 2, but this is not particulalry helpful in a real life application.

Answer 3

Hey there!

An exact value is a number that is an integer.

If a number turns out to be a decimal, then it is generally a terminating or repeating decimal.

Ex: 2, 0, 1/3, 2.5

An estimated value is a number which the numbers after the decimal points are truncated, or removed, into a specific digits of precision.

Ex: sqrt(2) can be approximated into 1.4.

Hope it helps!

Answer 4

square root of 4 is exactly 2. square root of 5 is estimated a bit more than 2.

Answer 5

This is what I think it is.
sqrt(49)=-7 or 7 exact
sqrt(29)=5.30516
You can never find a number that, when multiplied by itself would give you 29. You could get a number very close to 28.99999 or something of that nature. You're estimating the sqrt(29) by this approximation.

Answer 6

Exact - Exact number without having many decimals or estimation

Estimated - Number that is estimated to the nearest digit. Example: Radical 2 is about 1.4 because I estimated 1.414... to the nearest tenth.