Home › UP Board Class 10 › Mathematics › Which statement is correct about the number $5-\…
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.
Related questions
What is the derivative of $x^x$ for $x>0$?If $y=x^{\tan^{-1}x}$, then $\dfrac{dy}{dx}$ equalsThe derivative of $ in^{-1}x$ isThe derivative of $\cos^{-1}x$ isWhat is $\dfrac{d}{dx}(\tan^{-1}x)$?If $y=\dfrac{1}{x^n}$, then $\dfrac{dy}{dx}$ isWhich identity is correct?For the expression $ qrt{1-x^2}$, a useful trigonometric substitution is