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Locate \sqrt{5},\sqrt{10} and \sqrt{17} on the number line

Answers (1)

Step I-  Draw number line shown in the figure.
Let the point O represent 0 (zero) and point A represent 2 units from O.

Step II- Draw perpendicular AX from A on the number line and cut off arc AB = 1 unit
We have OA = 2 units and AB = 1 unit
Using Pythagoras theorem, we have.
OB2 = OA2 + AB2
OB2 = (2)2 + (1)2 = 5
     OB = \sqrt{5}
Taking O as the centre and OB = \sqrt{5} as radius draw an arc cutting the line at C.
Clearly, OC = OB = \sqrt{5}.
Hence, C represents \sqrt{5} on the number line.

Similarly for \sqrt{10}  and \sqrt{17}we can plot the points as follows:
\sqrt{10}= \sqrt{3^{2}+1^{2}}
\sqrt{17}= \sqrt{4^{2}+1^{2}}


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