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A square having one unit side, means a side of length 1. There for Pythagorean tells us a^2+b^2=c^2; so 1^2+1^2=c^2. Therefore c=sqrt(2) but the question asks for the square of the diagonal: (sqrt(2))^2=2. Answer: 2

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15y ago
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16y ago

It comes from triangles, and its the square root of 2 (1.41421356...) times the length of one side.

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14y ago

there are two diagonals in square

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13y ago

Two

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Q: The square of the diagonal of a square having one unit sides?
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Related questions

What is the length of the diagonal of a square with sides that have a length of 1 unit?

Using Pythagoras' theorem the answer is equal to the square root of 2.


Where did square roots come from?

They came from geometry. If you have a square whose sides are 1 unit long then its diagonal is sqrt(2) units long.


The area of a square is 0.5 hectare Its diagonal equals?

Its diagonal is 1 unit.


Who created square roots and cube roots?

The ancients - Egyptians or Greeks. They probably came across the square root of 2 when considering the diagonal of a square with sides of length 1. The cube root of 3 would have arisen, similarly, with the principal diagonal of a unit cube.


How do you get diagonal measurement of a 17x17 inch square?

You use the Pythagorean Theorem, which says that the square of the hypotenuse of a right triangle is the sum of the squares of the other two sides. Two adjacent sides of a square (or any rectangle) together with a diagonal form a right triangle. In the case of a square, the triangle is isosceles. Calling the length of a side of the square (17 inches) one unit, the theorem tells us that the hypotenuse is the square root of 2 units. Therefore the diagonal of the square is 17 times the square root of 2 inches, which is about 24 inches.


Why are percent rational numbers?

They need not be. A unit circle inside a square with sides of 2 units, for example, occupies 25*pi per cent of the area. But 25*pi is not a rational number.


What is a square with 1cm sides called?

It is a unit centimetre square.


Can you draw a rectangle that has an area of 6 square unit and a perimeter of 12 units?

Yes it measures 3 on all sides sides across from each other but it would have to be a square. Having a rectangle is impossible. Then again a square is a rectangle but a rectangle isn't a square.


What are the dimensions of largest square that can be inscribed in a circle?

The diagonal of the square is the diameter of the circle (think about it!) so the sides of the square can be pythagorassed ie the square of the diagonal is twice the square of a side. As an example, consider a circle of diameter 50 units. the square of this is 2500 so every side of the square is the square root of 1250 units which equals sqrt 625 x sqrt 2 or 25 root 2 ie 35.355339 units, or 70.71% of the diameter of the circle. More basically, the diagonal is the hypotenuse of a 45/45/90 triangle so the sides are in the ratio 1/1/root2 or if you want the hypotenuse to be 1, the sides would be (root 2)/2. Either way, the sides are root2 times the radius of the circle, which is of course half the diameter. This is in full agreement with the 25 root2 calculated above for a 50 unit diameter circle.


What is a real world example of a radical function?

The diagonal of a unit square, for example, is radical(2).


How do you locate the square root if two on a number line using geometry?

Draw a square which is 1 unit by 1 unit in size. By Pythagoras, the diagonal of the square will be sqrt(2) units in length.


How is radical used in real life?

In the simplest case, it is use to find the diagonal length of a unit square.