# 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

With O as the centre and
as radius draw an arc cutting real line at C. Clearly,
Thus, C represents 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 have
Now evaluate the square roots.
Therefore, we have,
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,

Thus, we can mark 2.7 on the number line as follows:

Thus, OA represents the square root of 7.3