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# Does an irrational number multiplied by an irrational number equal an irrational number?

Updated: 4/28/2022

Wiki User

15y ago

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.

Wiki User

15y ago

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Q: Does an irrational number multiplied by an irrational number equal an irrational number?
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### Is an irrational number plus an irrational number equal a rational or an irrational number?

An irrational number is a number that has no definite end. So it can't be multiplied or divided by anything to make a rational number that does have a definite end.

### Can a rational number be multiplied by an irrational number and equal a rational number?

Only if the rational number is 0.

### What will produce an irrational number when multiplied by 0.4?

Every irrational number, when multiplied by 0.4 will produce an irrational number.

### Which of the number will produce an irrational number when multiplied by 0.5?

Any irrational number, when multiplied by 0.5 will give an irrational number.

### What numbers will produce an irrational number when multiplied by 0.5?

Every irrational number, when multiplied by 0.5 will produce an irrational number.

### What numbers will produce an irrational number when multiplied by 0.4?

Every irrational number, when multiplied by 0.4 will produce an irrational number.

### Which number produces an irrational number when multiplied by 0.4?

Any irrational number will do.

### What is a rational number multiplied by an irrational number equal?

It can be a rational number or an irrational number. For example, sqrt(2)*sqrt(50) = 10 is rational. sqrt(2)*sqrt(51) = sqrt(102) is irrational.

### Which numbers will produce an irrational number when multiplied by 0.5?

Any irrational number multiplied by 0.5 will remain irrational. Any rational number multiplied by 0.5 will remain rational.

### Whether a rational number multiplied by an irrational number gives an irrational number?

rational * irrational = irrational.

### What produces an irrational number when multiplied by 0.5?

Any irrational number does.

### Why is it not possible for a whole number other than 0 multiplied by an irrational number to be equal a rational number?

It certainly is possible. For example, the square root of 2 times the square root of two is equal to two. Another example: pi multiplied by (1/pi) is equal to 1.Ans. 2No, it is not possible. The two 'counterexamples' above involve multiplying the irrational number by another irrational number. But, the question specifies multiplying the irrational number by a whole number other than zero. As long as you obey that restriction you are stuck with an irrational result.