No.
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The square root of 225 is 15, which is NOT an irrational number.
[ square root of (2) ] is irrational
The square root of 300 is irrational. Irrational numbers are infinitely dense and therefore the concept of consecutive numbers cannot be applied to irrational numbers.
Yes. For example, the square root of 3 (an irrational number) times the square root of 2(an irrational number) gets you the square root of 6(an irrational number)
The square root of 4725 is irrational!