To locate: the point 2 on a number line, explain the location of 5 and 6 , list some other irrational numbers can be located in same manner.

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1.1, Problem 84E
To determine

To locate: the point 2 on a number line, explain the location of 5 and 6 , list some other irrational numbers can be located in same manner.

Expert Solution

Explanation of Solution

Given information:

Given number line

Calculation:

If in a right triangle, the base=height=1 unit, then the hypotenuse is 2 units, by the Pythagorean theorem.

So, consider one unit from the origin along the positive direction of the x axis and from there, consider the point at a distance of one unit parallel to the y axis. We then get to a point which is 2 units from the origin.

Consider the distance to be radius of a circle, which intersects the x axis at 2 units.

Thus, the point of intersection of the circle with the x axis is 2 units.

Similarly, 2 units from the origin along the x axis and 1 unit parallel to y axis, the point we reach will be 5 units from the origin.

So by drawing a circle using this distance as the radius, it intersects the x axis at 5 units.

Thus, 5 can be traced on the x axis.

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