Show how √13 can be represented on the number line.

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Detailed Solution

Representing √13 on the Number Line

To locate √13 on the number line, we start by expressing 13 as a sum of two perfect squares:
- 13 = (3)² + (2)²
- 9 + 4 = 13
Draw a number line.
Consider OA = 3 units on the number line.
From point A, draw a perpendicular line AB such that AB = 2 units.
Join OB to form a right-angled triangle OAB.
Using the Pythagorean theorem:
- OB² = OA² + AB²
- OB² = 3² + 2²
- OB² = 9 + 4
- OB² = 13
Taking the square root, we get OB = √13.
Using a compass, with center O and radius OB, draw an arc that intersects the number line at point P.
The point P represents √13 on the number line.

Thus, √13 is represented on the number line.

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