Q: Is 2 over 3 irrational

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sqrt(2) is irrational. 3 is rational. The product of an irrational and a non-zero rational is irrational. A more fundamental proof would follow the lines of the proof that sqrt(2) is irrational.

The square roots of 2 and 3 are irrational but not transcendent.

Yes, multiplying a rational and an irrational number gives an irrational product. For example 3 * pi = 3pi = 9.424789... or 2 * sqrt 2 = 2^(3/2).

No, 3 is a rational number. Pi and the square root of 2 are irrational numbers.

No. It can be written as -2/3.

Related questions

No.3*sqrt(2) and sqrt(2) are irrational. But their quotient is 3, which is rational.

Rational (-1.5) Since it can be expressed as a fraction.

3/8 is rational, it can't be irrational.

-3

No. Two irrational numbers can be added to be rational. For example, 1/3 + 2/3 = 3/3. 1/3 and 2/3 are both irrational, but 3/3 = 1, which is rational.

sqrt(2) is irrational. 3 is rational. The product of an irrational and a non-zero rational is irrational. A more fundamental proof would follow the lines of the proof that sqrt(2) is irrational.

irrational 2/3 = .66666666 and so on

No. The easiest counter-example to show that the product of two irrational numbers can be a rational number is that the product of √2 and √2 is 2. Likewise, the cube root of 2 is also an irrational number, but the product of 3√2, 3√2 and 3√2 is 2.

300 = 2 x 2 x 3 x 5 x5 and sqrt(2) is irrational then sqrt(300) is irrational

No. In fact, the sum of conjugate irrational numbers is always rational.For example, 2 + sqrt(3) and 2 - sqrt(3) are both irrational, but their sum is 4, which is rational.

Not necessarily. 3+sqrt(2) and 3-sqrt(2) are both irrational numbers. Their sum is 6 - a rational.

sqrt(2)*sqrt(3) is an irrational product.