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First let us assume that
is an rational number
Step-by-step explanation:
then,
ie, √3= p/q-6
ie, √3=p-5q/q (where p and q are co-primes and q is not equal to zero)
Therefore p, q are integers,
therefore p-5q/q is a rational number
But we know that √3 is irrational
This contradiction has arisen because our assumption is wrong.
therefore √3 +5 is an irrational number
If it is not given in the question, also prove that √3 is irrational
hope this helps u:-)
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