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A cube has an edge length that is a rational number of centimeters, identifying which measurements will require t by e use of i...Asked by Keyzia Boone
A cube has an edge length, a, that is a rational number of centimeters, identify which measurement will require the use of irrational number.
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The measurement of the diagonal of the cube will require the use of an irrational number.
The diagonal of a cube is the line connecting two opposite vertices. If we consider the edge length of the cube, 'a', the diagonal can be found using the Pythagorean theorem in three dimensions.
By applying the theorem, we have:
diagonal² = a² + a² + a²
diagonal² = 3a²
diagonal = √(3a²)
Since 'a' is a rational number, the square root of 3 would be an irrational number. Thus, the measurement of the diagonal of the cube will involve the use of an irrational number.
The diagonal of a cube is the line connecting two opposite vertices. If we consider the edge length of the cube, 'a', the diagonal can be found using the Pythagorean theorem in three dimensions.
By applying the theorem, we have:
diagonal² = a² + a² + a²
diagonal² = 3a²
diagonal = √(3a²)
Since 'a' is a rational number, the square root of 3 would be an irrational number. Thus, the measurement of the diagonal of the cube will involve the use of an irrational number.
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