About irrational number

In summary, the answers for the given equations in terms of rational and irrational numbers are both irrational. This can be proven by assuming they are rational and then isolating the irrational number, which results in a contradiction. "Any +ve integer" refers to a positive integer.
  • #1
spidey
213
0
wat are the answers for these in terms of rational,irrational

(irrational number)*(any +ve integer) = ?
(any +ve integer) - (irrational number)*(any integer) = ?

are the answers also irrational numbers
 
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  • #2
But of course! Think about it. In both cases, pretend that they give rational numbers. Then isolate the irrational number. See the contradiction?
 
  • #3
What is "any +ve integer"?
 
  • #4
mathman said:
What is "any +ve integer"?

positive integer
 
  • #5
spidey said:
wat are the answers for these in terms of rational,irrational

(irrational number)*(any +ve integer) = ?
(any +ve integer) - (irrational number)*(any integer) = ?

are the answers also irrational numbers

Why not prove it.

In your first example start with

x*n=p/q

Dividing both sides by n gives:
X=p/(q*n) which implies x is rational which is a contradiction.
 
  • #6
Thanks John...so answer for first one is irrational so second should also be irrational...
 
  • #7
spidey said:
Thanks John...so answer for first one is irrational so second should also be irrational...

Apply the same method and work it out.
 

1. What is an irrational number?

An irrational number is a real number that cannot be expressed as a ratio of two integers. In other words, it cannot be written in the form of a fraction where the numerator and denominator are both whole numbers.

2. How is an irrational number different from a rational number?

A rational number can be written as a fraction, while an irrational number cannot. Rational numbers are also finite decimal numbers, while irrational numbers have an infinite number of non-repeating digits after the decimal point.

3. What are some examples of irrational numbers?

Some common examples of irrational numbers include pi (3.14159...), the square root of 2 (1.41421...), and the golden ratio (1.61803...). These numbers cannot be expressed as a fraction and have an infinite number of non-repeating digits after the decimal point.

4. Why are irrational numbers important in mathematics?

Irrational numbers are important because they allow us to represent values that cannot be expressed as fractions or decimals. They are also essential in many mathematical concepts, such as geometry, trigonometry, and calculus.

5. How are irrational numbers used in the real world?

Irrational numbers are used in many real-world applications, such as in engineering, physics, and finance. They are also used in measurements, such as calculating the circumference of a circle, and in computer programming to generate random numbers. Additionally, irrational numbers are used in the design of musical scales and in art to create aesthetically pleasing proportions.

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