Question

Which of the following iS ?

A

If is a rational number, such that the prime factorisation of denominator is not in the form , (where and are non-negative integers), then it has a decimal expansion which is non-terminating and repeating.

B

is an irrational number.

C

Every composite number can be expressed as a product of primes.

D

None of these

Easy

Solution

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Correct option is D)

(a)This is correct. Let the , then the prime factorization of 

, thus this fraction is terminating and non-repeating. 

Thus, the prime factorization of denominator of a rational number which is not of the form is non-terminating and repeating.

(b) let be a rational number and so 5+\sqrt { 2 } .$$ Then,



Since,  is irrational number. So, the contradiction is wrong that is rational number.
 
Hence is irrational number. 

(c) Every composite number can be expressed as a product of primes. This is also correct.

Hence option (d) is incorrect option.

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