Insert three irrational numbers between 2√3 and 2√5.

Insert three irrational numbers between 2√3 and 2√5, and arrange in descending order.

Solution:

Take the square

(2√3)² = 12 and (2√5)² = 20

So the number 13, 15, 18 lie between 12 and 20 between (√12)² and (√20)²

√13, √15, √18 lie between 2√3 and 2√5

Therefore, three irrational numbers between

2√3 and 2√5 are √13, √15, √18 or √13, √15 and 3√2.

Here

√20 ˃ √18 ˃ √15 ˃ √13 ˃ √12 or 2√5 ˃ 3√2 ˃ √15 ˃ √13 ˃ 2√3

Therefore, the descending order: 2√5, 3√2, √15, √13 and 2√3

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