Question

If $\sqrt{10+\sqrt{64}}=\sqrt{a+2\sqrt{b}}$ then value of $a$ and $b$ are

• A. $a=10$ and $b=64$
• B. $a=10$ and $b=16$
• C. $a=64$ and $b=10$
• D. $a=8$ and $b=2$

Answer 1

The correct option is B $a=10$ and $b=16$

$\sqrt{10+\sqrt{64}}=\sqrt{a+2\sqrt{b}}$

squaring both sides we get,

$\Rightarrow$ $10+\sqrt{64}=a+2\sqrt{b}$

$\Rightarrow$ $10+\sqrt{16\times 4}=a+2\sqrt{b}$

$\Rightarrow$ $10+2\sqrt{16}=a+2\sqrt{b}$

Comparing both sides,

$\Rightarrow$ $a=10$ and

$\Rightarrow$ $2\sqrt{b}=2\sqrt{16}$

$\therefore$ $b=16$