Let 'a' and 'b' be the length of one side and diagonal of a square.
Pythagorus's theorem as applied to a square: a^2 + a^2 = b^2.
Substituting a = 2 into the equation, we have b^2 = 2^2 + 2^2 = 8.
b = sqrt(8) = 2 * sqrt(2).
Q.E.D.
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30 radical 2
In the simplest case, it is use to find the diagonal length of a unit square.
By using Pythagoras: diagonal2 = side2 + side2 = side2 x 2 => diagonal = side x √2
The diagonal length of a square with a 900 square foot area is: 42.43 feet.
The diagonal of a unit square, for example, is radical(2).
It is believed that it arose as the measure of the diagonal of the unit square. By Pythagoras's theorem, the square of this length was 2, but when it turned out that this was not a rational number, it was expressed as a radical.
in a square it is the side length radical 2
30 radical 2
In the simplest case, it is use to find the diagonal length of a unit square.
By using Pythagoras: diagonal2 = side2 + side2 = side2 x 2 => diagonal = side x √2
As a square has right angles, the diagonal forms a right triangle with two of the sides of the square. Therefore use Pythagoras: diagonal² = side² + side² → diagonal² = 2side² → diagonal = side × √2 Therefore to find the length of the diagonal of a square, multiply the side length of a square by the square root of 2.
Divide the length of the diagonal of a square by 1.4142 (which is the square root of 2) to find the length of a side. Similarly, to find the length of the diagonal of a square, multiply the length of a side by 1.4142.
The diagonal length = 7.07 inches.
The diagonal length of a square with a 900 square foot area is: 42.43 feet.
The diagonal of a unit square, for example, is radical(2).
If the length of a side of the square is S units then the diagonal is S*sqrt(2) units in length.
To find the length of each diagonal of a square, divide the sum of the diagonal lengths by 2. Since a square has two diagonals of equal length, this division will give you the length of each diagonal.