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LocatedEXERCISE 1.21. State whether the following statements are true or false. Justify your answers.(1) Every irrational number is a real number.(1) Every point on the number line is of the form m, where m is a natural numbe(i) Every real number is an irrational number.Are the square roots of all positive integers irrational? If not give an example ofsquare root of a number that is a rational number.3. Show how 5 can be represented on the number line.Р.4. Classroom activity (Constructing the square rootspiralf): Take a large sheet of paper and constructthe 'square root spiral' in the following fashion. Start15with a point and draw a line segment OP, of unitlength. Draw a line segment PP, perpendicular toOP, of unit length (see Fig. 1.9). Now draw a linesegment PP, perpendicular to OP. Then draw a lineOsegment PP perpendicular to OP, Continuing inFig. 1.9: Constructingthis manner, you can get the line segment PP, bysquare root spiraldrawing a line segment of unit length perpendicular to OP In this manner, you wilhave created the points PP P... and joined them to create a beautiful spindepicting 2. 3. 4.... |
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