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?

9514 1404 393

  b.  275 cm³

Step-by-step 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.

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).