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olcyr
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Let p and q be distinct primes. Prove that [tex]\sqrt{p/q}[/tex] is a irrational number.
olcyr said:Let p and q be distinct primes. Prove that [tex]\sqrt{p/q}[/tex] is a irrational number.
Irrational numbers are numbers that cannot be expressed as a ratio of two integers. They are decimal numbers that do not terminate or repeat, such as pi (3.141592...) or the square root of 2 (1.414213...).
If a number cannot be written as a fraction with integers in the numerator and denominator, then it is irrational. Another way to identify irrational numbers is by finding their decimal representations, which will never terminate or repeat.
Rational numbers can be expressed as a ratio of two integers, while irrational numbers cannot. Rational numbers also have decimal representations that either terminate or repeat, while irrational numbers have decimal representations that never terminate or repeat.
Yes, irrational numbers can be both positive and negative. Examples of negative irrational numbers include -pi, -sqrt(2), and -e (2.718281...).
Irrational numbers play an important role in mathematics and science. They are used to solve problems in geometry, to describe the behavior of waves, and to calculate probabilities in statistics. They are also used in many real-life applications, such as engineering and finance.