- #1
courtrigrad
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http://www.artofproblemsolving.com/Forum/weblog.php?w=564
Could someone help me with 2b?
Thanks
Could someone help me with 2b?
Thanks
courtrigrad said:Ok, so [tex] p^{2} = rm^{2}q^{2} [/tex] and [tex] p^{2} [/tex] is divisible by [tex] rm^{2} [/tex]. So then I have to show that [tex] q^{2} [/tex] is also divisible by [tex] rm^{2} [/tex]. Is [tex] m [/tex] just any positive number?
Thanks
Irrational numbers are numbers that cannot be expressed as a ratio of two integers. They are non-repeating and non-terminating decimals. Examples of irrational numbers include pi (3.14159...) and the square root of 2 (1.41421...).
Rational numbers can be expressed as a ratio of two integers, while irrational numbers cannot. Rational numbers also have either a finite or repeating decimal representation, while irrational numbers have an infinite and non-repeating decimal representation.
Irrational numbers cannot be written as a fraction or ratio, so they are often identified by the presence of a non-repeating and non-terminating decimal representation. Additionally, square roots of non-perfect squares and numbers that do not have a pattern or repetition in their decimal representation are also irrational numbers.
Irrational numbers are used in various fields such as mathematics, physics, and engineering. They are used to calculate the circumference and area of circles, to model natural phenomena such as waves and vibrations, and to design efficient structures and processes.
Yes, irrational numbers can be approximated by rounding them to a certain number of decimal places. However, the exact value of an irrational number cannot be determined as it is infinite and non-repeating.