The numbers 8 and 23 are irrational number because they do not go into any more number than themselves. This is taught in math.
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No. sqrt(8) is irrational sqrt(2) is irrational but sqrt(8) /sqtr(2) = sqrt(4) = ±2 is not irrational.;
No. Square root of 23 is irrational.
The product will also be irrational.