MCQ
If $\sqrt{13-\text{a}\sqrt{10}}=\sqrt8+\sqrt5,$ then $a =$
- A$-5$
- B$-6$
- ✓$-4$
- D$-2$
✓
Answer
Correct option: C.
$-4$
$\sqrt{13-\text{a}\sqrt10}=\sqrt8+\sqrt5$
Squaring both sides, we get
$13-\text{a}\sqrt{10}=8+5+2\sqrt{40}$
$={13}-\text{a}\sqrt{10}-{13}=2\times2\sqrt{10}$
$=-\text{a}\sqrt{10}=4\sqrt{10}$
$\Rightarrow\text{a}=-4$
Hence, correct option is $(c).$
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