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Is the quotient of an irrational number and a rational number always irrational?
No. It is not defined if the rational number happens to be 0.
When an irrational number is divided by a rational number is the result rational or irrational?
It is irrational - unless the divisor is 0 in which case the division is not defined.
Is the square root of 51 irrational?
yes, it is irrational. An irrational number can defined as a number that can not be expressed as a finite nor a repeating decimal.
Can you give one example for surd which is not irrational?
It is impossible to have a surd that is not irrational. Surds are defined to be an irrational number (square root of a number).
Is 2.14 a rational number or irrational number?
Any number with a defined end point, including 2.14, is a rational number.
Why should a real number be rational or irrational?
Because irrational numbers are defined as real numbers which are not rational.
Why does a real number have to be rational or irrational?
Because irrational numbers are defined as all real numbers which are not rational.
Is every irrational number a real number and how?
The set of real numbers is defined as the union of all rational and irrational numbers. Thus, the irrational numbers are a subset of the real numbers. Therefore, BY DEFINITION, every irrational number is a real number.
Why does any real number must be either a rational number or an irrational number?
It is due to the fact that the set of real numbers is defined as the union of the rational and irrational numbers.
Is every irrational a real number. If Yes Why?
Yes irrational numbers are real numbers that are part of the number line,
Is 6.3478 a rational or irrational number?
Any number with a defined end-point, such as 6.3478, is, by definition, rational.
What can irrational numbers be defined as?
In mathematics, an irrational number is any real number which cannot be expressed as a fraction a/b, where a and b are integers, with b non-zero, and is therefore not a rational number
