How do you construct a segment that is the square root of 7 inches long since there are no two numbers that you can add together that equal 7 that have equal square. Would one side of the triangle equal 2 and the other the square root of 9?
a^2 + b^2 = c^2 ... (√7)^2 + 3^2 = 4^2
construct a 3" segment with a perpendicular at one end
at the other end strike a 4" radius arc
the arc intersects the perpendicular √7" from the right angle
To construct a segment that is the square root of 7 inches long, you can use geometric techniques. Here's how:
1. Draw a horizontal line segment AB.
2. From point A, draw a perpendicular line segment AC with length 2 inches.
3. From point C, draw a line segment CD that extends past point B.
4. Construct a perpendicular to line segment CD from point D, intersecting CD at point E.
5. Draw a line segment AE, which will be the desired segment with length equal to the square root of 7 inches.
To explain how this construction works:
- The line segment AC with a length of 2 inches represents the square root of 4, which is a known value.
- The line segment CD is extended to allow for the construction of a right-angled triangle with a hypotenuse equal to the square root of 7 inches.
- The perpendicular constructed from point D results in a right-angled triangle. The length of this perpendicular is the square root of 7, as the pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
- The line segment AE represents the square root of 7 inches, which is achieved by connecting point A to point E.
This construction demonstrates that there are methods to approximate the square root of 7 inches without explicitly calculating its decimal value.