prove that square root of 3+square root of 5 is an irrational.

Asked by poshi.mails | 20th Feb, 2019, 10:33: PM

Expert Answer:

Let us assume √3 + √5 is rational number
 
Hence   √3 + √5 = a/b  ..............(1)
 
where a and b are integers, there is no common factor between a and b
 
we write eqn.(1)  as,  √3  = (a/b) - √5  ........................(2)
 
By squaring both sides,  3 = (a2 / b2 ) + 5 - 2√5(a/b)
 
-2  -(a2 / b2 ) = -2√5(a/b)
 
(b/a) ( 2b2 + a2 )/(2b2)  = √5
 
we get LHS as rational number , but RHS is irrational number. This is contradiction.
 
Hence √3 + √5 is not a rational number. It is an irrational number

Answered by Thiyagarajan K | 21st Feb, 2019, 12:21: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.