​ Represent √ 6,√ 7,√ 8 on the number line. ​

Question

Represent \(\sqrt6,\sqrt7,\sqrt8\) on the number line.

Answer 1

Draw a number line and mark point O, representing zero, on it.

Then, for representing \(\sqrt6\)

Step 1: On point A, 2 unit distance away from O, 

Step 2:Draw a perpendicular to number line of 1 unit distance (as taken on number line).

Step 3:Mark the point as A. 

Step 4: Join B to O. line OB represent \(\sqrt5\)

Step 5: Put compass on O and B and by taking the radius cut number line with one needle still on O.

Step 6: Mark point as A₁. This line OA₁ represent \(\sqrt6\)

Step 7: Now draw 1 unit long perpendicular on A₁. And mark the end point as B₁. 

Step 8: Now OB₁ represent \(\sqrt7\)

Step 9: By following Step 5 now cut \(\sqrt7\) on number line.

Step 10: For \(\sqrt8\) Draw perpendicular on \(\sqrt7\) on number line and follow above steps