How to express root 1 geometrically
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We now show how to find √x for any given positive real number 'x' geometrically.
For example, let us assume x = 4.5
We shall now find √4.5 geometrically.
Mark the distance 4.5 units from a fixed point P on a given line to obtain a point Q such that PQ = 4.5 units.
From Q, mark a distance of 1 unit and mark the new point as R.
Find the mid-point of PR and mark that point as O.
Draw a semicircle with center O and radius OR.
Draw a line perpendicular to PR passing through Q and intersecting the semicircle at S.
Then, QS = √4.5
More generally, to find √x, for any positive real number x:
Mark Q so that
PQ = x units
Mark R so that QR = 1 unit.
Then, as we have done for the case x = 4.5, we have QS = √x
We can prove this result using the Pythagoras Theorem.
For example, let us assume x = 4.5
We shall now find √4.5 geometrically.
Mark the distance 4.5 units from a fixed point P on a given line to obtain a point Q such that PQ = 4.5 units.
From Q, mark a distance of 1 unit and mark the new point as R.
Find the mid-point of PR and mark that point as O.
Draw a semicircle with center O and radius OR.
Draw a line perpendicular to PR passing through Q and intersecting the semicircle at S.
Then, QS = √4.5
More generally, to find √x, for any positive real number x:
Mark Q so that
PQ = x units
Mark R so that QR = 1 unit.
Then, as we have done for the case x = 4.5, we have QS = √x
We can prove this result using the Pythagoras Theorem.
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