How to point root 2 on number line

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Step-by-Step Solution

Step 1: Draw a Number Line

First, draw a straight line and mark a point as 0. Then, mark another point to its right as 1, ensuring a unit distance between them. This establishes our scale on the number line.

Step 2: Construct a Perpendicular

At the point representing 1 on the number line, draw a line segment perpendicular to the number line. This segment should also have a length of 1 unit, matching the distance between 0 and 1.

Step 3: Form a Right-Angled Triangle

Now, connect the endpoint of the perpendicular segment (which is 1 unit above the point 1 on the number line) to the point 0 on the number line. This forms a right-angled triangle with two sides of length 1 unit.

Step 4: Apply Pythagorean Theorem

Using the Pythagorean theorem, the length of the hypotenuse of this right-angled triangle is $\sqrt{1^2 + 1^2} = \sqrt{2}$. This hypotenuse represents the distance from 0 to the endpoint of the perpendicular.

Step 5: Plot on Number Line

With 0 as the center and the length of the hypotenuse (which is $\sqrt{2}$) as the radius, draw an arc that intersects the number line. The point where the arc intersects the positive side of the number line is the location of $\sqrt{2}$.