Question

Represent (√9.3) on the number line.​

Answer 1

Step-by-step explanation:

Solution:

Let's look into the steps below to represent √9.3 on the number line.

Step I: Draw a line and take AB = 9.3 units on it.

Step II: From B, measure a distance of 1 unit and mark C on the number line. Mark the midpoint of AC as O.

Step III: With ‘O’ as center and OC as radius, draw a semicircle.

Step IV: At B, draw a perpendicular to cut the semicircle at D.

Step V: With B as a center and BD as radius draw an arc to cut the number line at E. Thus, taking B as the origin the distance BE = √9.3

Therefore, point E represents √9.3 on the number line.

Let's look at the proof shown below.

AB = 9.3, BC = 1

AC = AB + BC = 10.3

OC = AC/2 = 10.3/2 = 5.15

OC = OD = 5.15

OB = OC – BC = 5.15 - 1 = 4.15

In right-angled ∆OBD, using Pythagoras theorem we have,

BD2 = OD2 - OB2

= (5.15)2 - (4.15)2

= (5.15 + 4.15)(5.15 - 4.15) [Using a² - b² = (a + b)(a - b)]

= 9.3 × 1

= 9.3

Hence, BD = √9.3 = BE [Since they are the radii of the same circle]

Thus, we can say point E represents √9.3 on the number line.