Question

Which of the following iS $INCORRECT$?

• A. If $x$is a rational number, such that the prime factorisation of denominator is not in the form $2^n{5}^m$, (where $m$ and $n$ are non-negative integers), then it has a decimal expansion which is non-terminating and repeating.
• B. $5+\sqrt{2}$ is an irrational number.
• C. Every composite number can be expressed as a product of primes.
• D. None of these

Answer 1

Answer: (D)

(a)This is correct. Let the $\frac{17}{100}$, then the prime factorization of

$100=2^2\ast 5^2$, thus this fraction is terminating and non-repeating.

Thus, the prime factorization of denominator of a rational number which is not of the form $2^n\ast 5^m$ is non-terminating and repeating.

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

$⟹5+\sqrt{2}=\frac{a}{b}$

$⟹\sqrt{2}=\frac{a}{b}-5$

Since,$\sqrt{2}$ is irrational number. So, the contradiction is wrong that $\sqrt{2}$ is rational number.

Hence $5+\sqrt{2}$ 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.