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Question
`sqrt(2)/3` is a rational number.
Options
True
False
Solution
This statement is False.
Explanation:
Here `sqrt(2)` is an irrational number and 3 is a rational number, we know that when we divide irrational number by non-zero rational number it will always give an irrational number.
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Classroom activity (Constructing the ‘square root spiral’): Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion. Start with a point O and draw a line segment OP1 of unit length. Draw a line segment P1 P2 perpendicular to OP1 of unit length. Now draw a line segment P2 P3 perpendicular to OP2. Then draw a line segment P3 P4 perpendicular to OP3. Continuing in this manner, you can get the line segment Pn–1Pn by drawing a line segment of unit length perpendicular to OPn–1. In this manner, you will have created the points P2, P3,...., Pn,.... ., and joined them to create a beautiful spiral depicting `sqrt2, sqrt3, sqrt4,` ...
