How would you find root 2? I have been told to use a number line. I have tried to visualize it on a number line using triangles. But am unsure of where to go from there.
2025-01-12 23:30:36.1736724636
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Square root of two
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The square root of two can not be expressed as a fraction of whole numbers or as a decimal. It is the classic example of an irrational number. The real numbers are infinite limits of rationals but the irrationals can not be expressed completely in any finite form. Geometrically the diagonal of a square with sides of one unit, will be the square root of two units. The square root can be estimated as about 1.414... but the decimal never ends doesn't repeat cyclically.
Draw an isosceles triangle rectangle with length 1 on real line. Using the Pythagorean Theorem, you can see that its hypotenuse measures $\sqrt{2}$. Now draw a circle with center in the origin of real line and radius $\sqrt{2}$. Finally the intersection between and positive real line and the circle will be in the position of $\sqrt{2}$.