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Is the square of an irrational number rational?
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.
Is an irrational number times an irrational number always irrational?
The square root of 2 is irrational, yet the product of it with itself is 2. So the answer is no.
Is an irrational number closed under division?
No. sqrt(8) is irrational sqrt(2) is irrational but sqrt(8) /sqtr(2) = sqrt(4) = ±2 is not irrational.;
Can 2 irrational add to an irrational number?
Yes. The sum of two irrational numbers can be rational, or irrational.
Why is 3 square root of 2 is irrational?
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.
Is the square of an irrational number rational?
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.
Does an irrational number multiplied by an irrational number equal an irrational number?
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.
Is a rational number times a irrational number?
Can be irrational or rational.1 [rational] * sqrt(2) [irrational] = sqrt(2) [irrational]0 [rational] * sqrt(2) [irrational] = 0 [rational]
Is the sum of irrational roots irrational?
Not always. For example: sqrt(2)+(-sqrt(2))=0 which is not irrational.
Will any irrational number divided by an irrational number be irrational?
No.3*sqrt(2) and sqrt(2) are irrational. But their quotient is 3, which is rational.
Is an irrational number times an irrational number always irrational?
The square root of 2 is irrational, yet the product of it with itself is 2. So the answer is no.
Is an irrational number closed under division?
No. sqrt(8) is irrational sqrt(2) is irrational but sqrt(8) /sqtr(2) = sqrt(4) = ±2 is not irrational.;
Can you add two positive irrational numbers to get an irrational number?
Yes. sqrt(2) + sqrt(2) = 2*sqrt(2), an irrational number.
How can be the product of 2 irrational numbers a rational numbers 5?
5*sqrt(2) is one irrational number. 1/sqrt(2) is another irrational number.Their product is 5!5*sqrt(2) is one irrational number. 1/sqrt(2) is another irrational number.Their product is 5!5*sqrt(2) is one irrational number. 1/sqrt(2) is another irrational number.Their product is 5!5*sqrt(2) is one irrational number. 1/sqrt(2) is another irrational number.Their product is 5!
Is the square root of 300 rational or irrational?
300 = 2 x 2 x 3 x 5 x5 and sqrt(2) is irrational then sqrt(300) is irrational
Can 2 irrational add to an irrational number?
Yes. The sum of two irrational numbers can be rational, or irrational.
Why is 3 square root of 2 is irrational?
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.
