Question

given a segment of unit length, construct a segment of length square root of 7.

Answer 1

Draw line and mark 1 unit length AB on it.
Draw a perpendicular of 1 unit at B. Join AC. Now we will use the Pythagorean theorem to find AC

AC² = BC² + AB²

= 1 + 1

= 2

AC = √2 units

This is the representation of the square root of 2.

Now again at point C, we will draw a perpendicular CD of 1 unit length and then join DA.  

We will again Pythagorean theorem to find AD.

AD² = AC² + CD²

= (√2)² + 1²
= 2 +1

= 3

AD = √3 units

This is the representation of square root of 3.

Now we will repeat the same thing by drawing a perpendicular DE of 1 unit length.

So. EA² = DA² + DE²
EA² = 3 + 1

EA = √4 units = 2 units ( This is representation of sqaure root of 4)

Now again we draw a perpendicular EF and find FA as √5 units using the same method.

FA² = AE² + FE² = 4 + 1

FA = √5 units

Following the same, we get FG as √6 unit.



Finally, we draw a perpendicular GH of 1 unit and find HA following the same method.

HA² = GA² + HG²
HA² = (√6)² + 1²
HA² = 7

HA = √7 units

And this represents the square root of seven.