If 13-a10 = 8+ 5, then a = - Vidyadip

Question

If $\sqrt{13-\text{a}\sqrt{10}}=\sqrt8+\sqrt5,$ then a =

✓

Answer

-4
Solution:
$\sqrt{13-\text{a}\sqrt10}=\sqrt8+\sqrt5$
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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