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Let $AB = 1$, $AD=a$. We draw another line at any angle with $AB$, mark a point C on it such that $AC=a$. Let a line through $D$ parallel to $BC$ meet this line at $E$enter image description here, then $AE=a^2$, continuing this way we can raise it to any integer power.

Using this you can only calculate negative integral powers as well. Calculation of square roots is simple so we can construct all numbers of form $a^\frac{n}{2}$. But we cannot go cube roots or anything as using scale and compass we are limited to square roots.

Let $AB = 1$, $AD=a$. We draw another line at any angle with $AB$, mark a point C on it such that $AC=a$. Let a line through $D$ parallel to $BC$ meet this line at $E$enter image description here, then $AE=a^2$, continuing this way we can raise it to any integer power.

Let $AB = 1$, $AD=a$. We draw another line at any angle with $AB$, mark a point C on it such that $AC=a$. Let a line through $D$ parallel to $BC$ meet this line at $E$enter image description here, then $AE=a^2$, continuing this way we can raise it to any integer power.

Using this you can only calculate negative integral powers as well. Calculation of square roots is simple so we can construct all numbers of form $a^\frac{n}{2}$. But we cannot go cube roots or anything as using scale and compass we are limited to square roots.

Source Link
user345851
user345851

Let $AB = 1$, $AD=a$. We draw another line at any angle with $AB$, mark a point C on it such that $AC=a$. Let a line through $D$ parallel to $BC$ meet this line at $E$enter image description here, then $AE=a^2$, continuing this way we can raise it to any integer power.