Question

If $a+\sqrt{b}=\sqrt{c}$ where $aϵ0$ and $\sqrt{b}$ and $\sqrt{c}$ are surds, then_______

• A. $a=0$ and $b=c$
• B. $a=c$ and $b=0$
• C. $a=b$ and $b=c$
• D. $a=0$ and $b=0$

Answer 1

The correct option is A $a=0$ and $b=c$

$a+\sqrt{b}=\sqrt{c}$

Since $\sqrt{b}$ and $\sqrt{c}$ are surds

$a=0$

$\therefore \sqrt{b}=\sqrt{c}$

$\therefore b=c$