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Which statement is correct about the number $5-\sqrt{3}$?
AIt is rational because 5 is rational
BIt is irrational because subtracting an irrational number from a rational number gives an irrational number here
CIt is an integer
DIt is rational because $\sqrt{3}$ is less than 5
Answer & Solution
Correct answer: B. It is irrational because subtracting an irrational number from a rational number gives an irrational number here
If $5-\sqrt{3}$ were rational, then rearranging would give $\sqrt{3}=5-(5-\sqrt{3})$, which would be rational as a difference of rational numbers. But $\sqrt{3}$ is irrational. Hence $5-\sqrt{3}$ must be irrational.
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