(3) Represent the numbers root 5 and root 10 on a number line.
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Consider a number line. Let the point O represent 0 and point A represent 3.Now draw a perpendicular AP at A on the number line and cut off arc AB = 1 unit.Using Pythagoras Theorem, we have
OB(square) = OA(square) + AB(square)
= OB(square) = (3)square + (1)square
= OB(square) = 10
OB = root10
With O as the centre and as radius draw an arc cutting real line at C. Clearly, OC = OB = root10
Thus, C represents root10 on number line..
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