Irrational Numbers are infinitely dense. this means that there are infinitely many irrational numbers between any two numbers and so the term "next" has no meaning.
Next to any rational number is an irrational number, but next to an irrational number can be either a rational number or an irrational number, but it is infinitely more likely to be an irrational number (as between any two rational numbers are an infinity of irrational numbers).
Sometimes. eg the irrational number √2 squared is 2 which is rational (2 = 2/1) eg the irrational number √(√2) squared is √2 which is irrational.
The product of two irrational numbers may be rational or irrational. For example, sqrt(2) is irrational, and sqrt(2)*sqrt(2) = 2, a rational number. On the other hand, (2^(1/4)) * (2^(1/4)) = 2^(1/2) = sqrt(2), so here two irrational numbers multiply to give an irrational number.
No.3*sqrt(2) and sqrt(2) are irrational. But their quotient is 3, which is rational.
The square root of 2 is irrational, yet the product of it with itself is 2. So the answer is no.
Any irrational number multiplied by 0.5 will produce another irrational number. For example, if you take the irrational number √2 and multiply it by 0.5, you get 0.5√2, which is also irrational. Thus, any irrational number, when multiplied by 0.5, will result in an irrational number.
Can be irrational or rational.1 [rational] * sqrt(2) [irrational] = sqrt(2) [irrational]0 [rational] * sqrt(2) [irrational] = 0 [rational]
Yes. sqrt(2) + sqrt(2) = 2*sqrt(2), an irrational number.
Any irrational number, added to 0.4 will give an irrational number.
Any irrational number multiplied by 0.4 will produce an irrational number. For example, if you take the irrational number √2 and multiply it by 0.4, the result, 0.4√2, will also be irrational. Thus, any irrational number you choose will suffice.
irrational
Yes, the square root of 2 is an irrational number.