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Find a rational approximation for the edge lengths given as radical expressions for the rectangular prism. Which is the best estimation for the volume of prism using rational numbers approximations?

Find a rational approximation for the edge lengths given as radical expressions for-example-1
User Ramashankar
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1 Answer

19 votes
19 votes

9514 1404 393

Answer:

b. 275 cm³

Explanation:

A calculator is only capable of rendering rational approximations, so you can use your calculator to find the product of the edge dimensions, and the result will be a result obtained using rational approximations.

Perhaps, you're supposed to pick decimal fractions rounded to 1 or 2 decimal places. Those approximations might be ...

√23 ≈ 4.80

√27 ≈ 5.20

√125 ≈ 11.18

So, the volume is about (4.8)(5.2)(11.18) cm³ ≈ 279 cm³.

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If you use mixed-number values for the approximate square roots, you might use ...

√23 ≈ 4 7/9

√27 ≈ 5 2/11

√125 ≈ 11 4/23

Then the volume is about ...

(4 7/9)(5 2/11)(11 4/23) = 276 485/759 ≈ 276.6 . . . cm³

Since these rational approximations of the roots are all low by some amount, we know this estimate of the volume is a little low.

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We find the answer choices too blurry to read, but perhaps this is a match with what we think the second choice is: 275 cm³.

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Additional comment

For a number n, the square root can be approximated by ...

√n = √(a² +b) ≈ a +b/(2a+1) . . . . where 'a' is an integer and b < 2a+1

This estimate is always low (for b > 0).

User Hiropon
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