Answer:
Explanation:
therefore it can be written in form of a and b where a and b are co-prime numbers. 5a/b is rational number as it is of the form p/q which is a rational number. but we know that √3 is irrational number so our assumption is wrong. 2√3/5 is irrational.
Prove that 2 root 3 divided by 5 is irrational: a/b is a rational number, therefore 5a / 2b is also a rational number, but [tex]\sqrt{3}[/tex] is irrational number.
An irrational number is the number that cannot be expressed as a fraction for any integers and it have the decimal expansions that neither terminate nor periodic. Whereas a rational number is a number that expressed as a fraction where the numerator and the denominator in the fraction are integers.
Examples of rational numbers are, 0, 1, 1/2, 22/7, 12345/67, etc. Whereas pi the square root of two cannot be expressed as a fraction of two whole numbers, therefore they are both irrational. Numbers between 1 and 6 too also have infinite irrational numbers
The form is a/b where a and b are integers.
[tex]\frac{2\sqrt{3} }{5} = \frac{a}{b} [/tex]
[tex]\frac{2\sqrt{3} }{5} *5 = \frac{a}{b} * 5\\2\sqrt{3} = \frac{5a}{b}[/tex]
[tex]\sqrt{3} = \frac{5a}{2b}[/tex]
Because a/b is a rational number, therefore 5a / 2b is also a rational number.
Therefore, [tex]\sqrt{3}[/tex] should also be a rational number.
But this contradicts that [tex]\sqrt{3}[/tex] is irrational number.
So therefore [tex]\frac{2\sqrt{3} }{5}[/tex] is an irrational number.
Hope it helps! :)
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