How to solve root 10 and 7.3 on number line

how to solve root 10 and 7.3 on number line

Consider a number line. Let the point O represent 0 and point A represent 3.
Now draw a perpendicular AP at A on the number line and cut off arc AB = 1 unit.
Using Pythagoras Theorem, we have
image
image
With O as the centre andimage
as radius draw an arc cutting real line at C. Clearly,image
Thus, C represents image on the number line.
Now let us find the square root of 7.3
Make a list of perfect squares, 0, 4, 9, 16, 25, 36, …
Identify perfect squares closest to 7.3
Thus we have, 4 < 7.3 < 9
Take a positive square root of each number.
Thus, we haveimage
Now evaluate the square roots.
Therefore, we have,image
Now make a list of perfect squares between 2 and 3.

Numbers Squares
2.1 4.41
2.2 4.84
2.3 5.29
2.4 5.76
2.5 6.25
2.6 6.76
2.7 7.29
2.8 7.84
2.9 8.41

Thus, from the list it is clear that, 7.29 is closer to 7.3.
Therefore, we have,
image
Thus, we can mark 2.7 on the number line as follows:
image
Thus, OA represents the square root of 7.3