Question

For $\sqrt{4+\sqrt{83}}$, the correct option is .....................

• A. Does not exist as quadratic surd
• B. Does not exist as real numbers
• C. $2+\sqrt{83}$
• D. $\sqrt{83}-2$

Answer 1

The correct option is A Does not exist as quadratic surd

$\sqrt{4+\sqrt{83}}=\sqrt{4+2\sqrt{\frac{83}{4}}}$
Let, $a=4,b=\frac{83}{4}$
$⟹a^2-4b=16-4\left(\frac{83}{4}\right)=16-83=-67$
$\therefore$ $a^2-4b$ is not a perfect square
$\sqrt{4+\sqrt{83}}$ is not a quadratic surd.