CBSE Class 10 Answered
prove that 
+
is an irrational.
Asked by poshi.mails | 20 Feb, 2019, 22:33: 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 | 21 Feb, 2019, 00:21: AM
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