CBSE BoardEnglish MediumSTD 10MathsMODEL PAPER 7 (BASIC)1 Mark
MCQ
$2-\sqrt{3}$ is
✓
an irrational number
B
an integer
C
a rational number
D
a whole number
✓
Answer
Correct option: A.
an irrational number
Explanation:
Let $2-\sqrt{3}$ be rational number
$2-\sqrt{3}=\frac{p}{q}$ where $p$ and $q$ are composite numbers
$\sqrt{3}=\frac{p}{q}+2$
$\sqrt{3}=\frac{(p+2 q)}{q}$
since $p , q$ are integers, so $\frac{(p+2 q)}{q}$ is rational
$\therefore \sqrt{3}$ is an irrational number
it shows our supposition was wrong
hence $2-\sqrt{3}$ is an irrational number.
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