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The construction of a line segment of length √2 on the number line uses:
AA magic ruler that measures irrational numbers directly
BA right triangle with both legs of length 1: by Baudhāyana–Pythagoras, the hypotenuse equals √2; an arc of that length is then marked off on the number line
CSubtracting 1 from 3
DA trial-and-error decimal estimate
Answer & Solution
Correct answer: B. A right triangle with both legs of length 1: by Baudhāyana–Pythagoras, the hypotenuse equals √2; an arc of that length is then marked off on the number line
To construct √2: draw OA = 1 unit, draw a perpendicular at A of length AB = 1. Then OB² = 1² + 1² = 2, so OB = √2 by Baudhāyana–Pythagoras. Draw an arc of radius OB centred at O, intersecting the number line at P — that point P is at distance √2 from O. This shows irrationals have geometric existence on the number line.
Related questions
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