Question

Simplified result of $\sqrt{200}-\sqrt{98}$ is

• A. $3\sqrt{2}$
• B. $10\sqrt{2}$
• C. $7\sqrt{2}$
• D. $-3\sqrt{2}$
• E. (b) and (c) above.

Answer 1

The correct option is A $3\sqrt{2}$

$\sqrt{200}-\sqrt{98}=\sqrt{2\times 100}-\sqrt{2\times 49}$

Note: $\sqrt{ab}=\sqrt{a}\times \sqrt{b}$

$\sqrt{200}-\sqrt{98}=\sqrt{2\times 100}-\sqrt{2\times 49}$
$=\sqrt{2}\times \sqrt{100}-\sqrt{2}\times \sqrt{49}$
$=\sqrt{2}\times \sqrt{{10}^2}-\sqrt{2}\times \sqrt{7^2}$
$=10\sqrt{2}-7\sqrt{2}$
$=(10-7)\sqrt{2}$
$=3\sqrt{2}$