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Question

# Represent √9.3 on the number line.

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Solution

## Step 1: Draw a line segment of unit 9.3. Extend it to C such that BC is 1 unit. Step 2: Now, AC = 10.3 units. Find the centre of AC and name it as O. Step 3: Draw a semi-circle with radius OC and centre O. Step 4: Draw a perpendicular line BD to AC at point B which intersects the semicircle at D. Also, Join OD. Step 5: Now, OBD is a right-angled triangle. Here, OD=10.32 (radius of semi-circle), OC=10.32, BC = 1 OB = OC – BC = (10.32) – 1 = 8.32 Using Pythagoras theorem, OD2=BD2+OB2 ⇒(10.32)2=BD2+(8.32)2⇒BD2=(10.32)2−(8.32)2⇒BD2=(10.32−8.32)(10.32+8.32)⇒BD2=9.3⇒BD=√9.3 Thus, the length of BD is √9.3. Step 6: Taking BD as radius and B as centre draw an arc which touches the line segment. The point where it touches the line segment is at a distance of √9.3 from B as shown in the figure.

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