No.
sqrt(8) is irrational
sqrt(2) is irrational but sqrt(8) /sqtr(2) = sqrt(4) = ±2 is not irrational.;
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No. You can well multiply two irrational numbers and get a result that is not an irrational number.
No, it is not. Root2 and root 8 are each irrational. Root8 / root2 =2. 2 is not a member of the set.
The whole numbers are not closed under division! The statement is false since, for example, 2/3 is not a whole number.
If a set is closed under an operation. then the answer will be a part of that set. If you add, subtract or multiply any two rational numbers you get another national number. But when it comes to division, it is closed except for one number and that is ZERO. eg 3.56 (rational number) ÷ 0 = no answer. Since no answer is not a rational number, that rational numbers are not closed under the operation of division.
No, whole numbers are not closed under division. It is possible to divide one whole number by another whole number and get a result which is not a whole number, for example, 1/2. One divided by two is a half.