Show how √7 can be represented on the number line.

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Detailed Solution

Representing √7 on the Number Line

Draw a line segment OB of 2 cm on the number line.
At point B, draw a perpendicular line BC of 1 cm.
Join OC to form a right-angled triangle OBC. The hypotenuse OC will be √5 (since √(2² + 1²) = √5).
Use a compass to mark the length of √5 on the number line.
Using √5 as the base and 1 cm as the adjacent side, draw another right-angled triangle. The hypotenuse will be √6.
Using √6 as the base and 1 cm as the adjacent side, draw another right-angled triangle. The hypotenuse will be √7.
Take the length of the hypotenuse √7 and mark the same length from 0 on the number line.

This point on the number line represents √7.