Question

Is √21 real number, rational number, whole number, Integer, Irrational number?

Answer 1

√21 real number, rational number, whole number, Integer, Irrational number?

it is a real number as well as a rational number

Answer 2

1st of all let us understand what are the definitions of them.

Real number : The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as √2 (1.41421356..., the square root of 2, an irrational algebraic number). Included within the irrationals are the transcendental numbers, such as π (3.14159265...). It includes all type of numbers like rational, irrational, whole, Natural, integers.

Rational number : Rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number.

Whole number : The positive integers.. Whole number set is {0,1,2,3,4,5.........}

Integer : an integer is number that can be written without a fractional component. i.g. 1, 2, 0, - 9, 2975, -890543.

Irrational number : It is a real number which is not rational. I.e they don't have p/q form. They may have non terminating non recurring end. E.g

$\sqrt{2} \: \: \: \sqrt{3} \: \: \: \sqrt{7} \: \: \: \sqrt{10}$

Hence

$\sqrt{21} \: is \: multipication \: of \: two \: irrational \\ numbers. \\ \sqrt{21} = \sqrt{7 \times 3} = \sqrt{7} \times \sqrt{3} \\ \\ thats \: why \: \sqrt{21} \: is \: an \: irrational \\ number....$