On a spiral construction (the 'square root spiral'), each new right triangle adds a hypotenuse of √n. Starting from a unit segment, the hypotenuses formed in order are √2, √3, √4, √5, ... Among the first five hypotenuses (√2 to √6), how many represent irrational lengths?

Question

Accepted Answer

4. The first five hypotenuses are √2, √3, √4, √5, √6. √4 = 2 is rational; the other four (√2, √3, √5, √6) are irrational. So 4 are irrational.

On a spiral construction (the 'square root spiral'), each new right triangle adds a hypotenuse of $n$ .
Starting from a unit segment, the hypotenuses formed in order are $2, 3, 4, 5$ , ...
Among the first five hypotenuses $(2$ to $6$ ), how many represent irrational lengths?

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More Class 9 Rational and Irrational Numbers practice

On a spiral construction (the 'square root spiral'), each new right triangle adds a hypotenuse of n​.Starting from a unit segment, the hypotenuses formed in order are 2​,3​,4​,5​, ...Among the first five hypotenuses (2​ to 6​), how many represent irrational lengths?

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 9 Rational and Irrational Numbers practice

On a spiral construction (the 'square root spiral'), each new right triangle adds a hypotenuse of $n$ .
Starting from a unit segment, the hypotenuses formed in order are $2, 3, 4, 5$ , ...
Among the first five hypotenuses $(2$ to $6$ ), how many represent irrational lengths?