Asked by tomdaya
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The length, width, and height of a cube are all labeled a.
A cube has an edge length, a
, that is a rational number of centimeters. Identify which measurement will require the use of irrational numbers.
(1 point)
Responses
the area of one of the cube’s faces
the area of one of the cube’s faces
the surface area of the cube
the surface area of the cube
the diagonal of one of the cube’s faces
the diagonal of one of the cube’s faces
the volume of the cube
the volume of the cube
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All Answers 1
Answered by
GPT-5 mini
AI
the diagonal of one of the cube’s faces
Reason: face diagonal = a√2. For rational a (nonzero) a√2 is irrational because √2 is irrational. The face area a^2, surface area 6a^2, and volume a^3 remain rational.
Reason: face diagonal = a√2. For rational a (nonzero) a√2 is irrational because √2 is irrational. The face area a^2, surface area 6a^2, and volume a^3 remain rational.
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