Question

If $\sqrt{13-a\sqrt{10}}=\sqrt{8}+\sqrt{5}$, then a =

• A. -5
• B. -6
• C. -4
• D. -2

Answer 1

The correct option is C

-4

$\sqrt{13-a\sqrt{10}}=\sqrt{8}+\sqrt{5}$

$\Rightarrow \sqrt{8+5-a\sqrt{10}}=\sqrt{8}+\sqrt{5}$

Squaring both sides,

$(\sqrt{8+5-a\sqrt{10}}{)}^2=(\sqrt{8}+\sqrt{5}{)}^2$

$\Rightarrow 8+5-a\sqrt{10}=8+5+2\times \sqrt{8}\times \sqrt{5}$

$\Rightarrow -a\sqrt{10}=2\sqrt{40}=2\times \sqrt{4\times 10}$

$\Rightarrow -a\sqrt{10}=2\times 2\times \sqrt{10}$

$\Rightarrow -a\sqrt{10}=4\sqrt{10}$

Comparing, we get

-a =4 $\Rightarrow$ a = -4