It is a real rational negative integer number whose value is -3
No, it is rational. Numbers whose decimal digits either stop or repeat can be written as a fraction and so are rational.
root 2 * root 2 = 2
There are very many uses for irrational numbers. A square, whose sides are a rational number, will have a diagonal of irrational length. The diagonals of most rectangles, with rational sides, will be irrational. The circumference and area of a circle (or ellipse) is related to pi, an irrational number. In the same way that pi is central to geometry, another irrational number, e, is fundamental to advanced calculus.
Certainly. Otherwise, there would be a rational number whose square was an irrational number; that is not possible. To show this, let p/q be any rational number, where p and q are integers. Then, the square of p/q is (p^2)/(q^2). Since p^2 and q^2 must both be integers, their quotient is, by definition, a rational number. Thus, the square of every rational number is itself rational.
It's rational. It can be written as the quotient of two numbers whose HCF is one.
It is a real rational negative integer number whose value is -3
No, it is rational. Numbers whose decimal digits either stop or repeat can be written as a fraction and so are rational.
There are very many uses for them. A square, whose sides are a rational number, will have a diagonal of irrational length. The diagonals of most rectangles, with rational sides, will be irrational. The circumference and area of a circle (or ellipse) is related to pi, an irrational number. In the same way that pi is central to geometry, another irrational number, e, is fundamental to advanced calculus.
There are very many uses for irrational numbers. A square, whose sides are a rational number, will have a diagonal of irrational length. The diagonals of most rectangles, with rational sides, will be irrational. The circumference and area of a circle (or ellipse) is related to pi, an irrational number. In the same way that pi is central to geometry, another irrational number, e, is fundamental to advanced calculus.
root 2 * root 2 = 2
Square root of a rational number may either be rational or irrational. For example 1/4 is a rational number whose square root is 1/2. Similarly, 4 is 4/1 which is rational and the square root is 2 which of course is also rational. However, 1/2 and 2 are rational, but their square roots are irrational. We can say the square root of a rational number is always a real number. We can also say the rational numbers whose square roots are also rational are perfect squares or fractions involving perfect squares.
There are very many uses for irrational numbers. A square, whose sides are a rational number, will have a diagonal of irrational length. The diagonals of most rectangles, with rational sides, will be irrational. The circumference and area of a circle (or ellipse) is related to pi, an irrational number. In the same way that pi is central to geometry, another irrational number, e, is fundamental to advanced calculus.
There are very many uses for irrational numbers. A square, whose sides are a rational number, will have a diagonal of irrational length. The diagonals of most rectangles, with rational sides, will be irrational. The circumference and area of a circle (or ellipse) is related to pi, an irrational number. In the same way that pi is central to geometry, another irrational number, e, is fundamental to advanced calculus.
Certainly. Otherwise, there would be a rational number whose square was an irrational number; that is not possible. To show this, let p/q be any rational number, where p and q are integers. Then, the square of p/q is (p^2)/(q^2). Since p^2 and q^2 must both be integers, their quotient is, by definition, a rational number. Thus, the square of every rational number is itself rational.
There are very many uses for irrational numbers. A square, whose sides are a rational number, will have a diagonal of irrational length. The diagonals of most rectangles, with rational sides, will be irrational. The circumference and area of a circle (or ellipse) is related to pi, an irrational number. In the same way that pi is central to geometry, another irrational number, e, is fundamental to advanced calculus.
1 + pi, 1 - pi. Their sum is 2.