No, they are not.
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Yes as for example if the rectangle has sides of square root 8 and square root 2 which are two irrational numbers but when multiplied it gives an area of 4 square units which is a rational number.
The square root of 25 is 5. 5 is a rational number. A rational number is a whole integer, like 3 or 5 or -8. Also, 4.333333... is a rational number because we know exactly what the number is. We know the number is 4 and 1/3, nothing more, nothing less. An irrational number is a number that goes on and on, with no specific pattern. A famous irrational number is pi. 3.14159....... Another example would be 453.788192742917471085723.......... Or 2.10100100010000100000........
The whole number closest to the square root of 65 is 8. The whole number closest to the square root of 65 is 8.
Rational. √(1/64) = 1/√64 = 1/8
The answer is not a rational number. It's the twice the square root of 1/pi inches, which comes out to just about 1 1/8".