- A√5
- B3
- C2√2
- D√10
Step-by-Step Solution
Compare squares: . From left to right the order is , so Q (second) is .
Answer: C) 2√2
The points P, Q, R and S mark the numbers √10, 2√2, √5 and 3, in some order. Which number does the orange point Q mark?
Class 9Number SystemsNumber Systems
Key idea: Representing real numbers on the number line
Every real number has a unique location on the number line.
- Rationals: easy to plot. → 3 quarters past 0.
- Irrationals like can be plotted geometrically: a right triangle with legs 1 and 1 has hypotenuse (Pythagoras). Use a compass to mark off on the number line from 0.
You can extend this — from a triangle with legs and 1, from legs 2 and 1, etc. (the spiral of Theodorus).
- Rationals: easy to plot. → 3 quarters past 0.
- Irrationals like can be plotted geometrically: a right triangle with legs 1 and 1 has hypotenuse (Pythagoras). Use a compass to mark off on the number line from 0.
You can extend this — from a triangle with legs and 1, from legs 2 and 1, etc. (the spiral of Theodorus).
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