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\sqrt{117} =  \sqrt{36 + 81} =  \sqrt{(6)^{2} + (9)^{2}}

So what this suggest? It means if we have a Right Angle Triangle with
(1) Base = 6, Height = 9
(2) Base = 9, Height = 6
The Hypotenuse will be \sqrt{117}

Now see the figure.... and follow the steps
(1) Draw line parallel to Y-axis from a mark at x = 6 (Blue Line)
(2) Draw line parallel to X-axis from a mark at y = 9 (Red Line)
(3) The Green Line is the hypotenuse of the required length.
(4) Now get the compass and take the measure of hypotenuse from the origin.
(5) Mark the arc using the compass on the X-axis (Brown Point)

You are done :)
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