147th Problem 2017

$\sqrt{32}+\sqrt{18}-\sqrt{50}=?$

Factor the terms inside the square root sign in terms of perfect squares.

$\sqrt{16(2)}+\sqrt{9(2)}-\sqrt{25(2)}=4\sqrt{2}+3\sqrt{2}-5\sqrt{2}=$ $\color{#EC7300}\large\boxed{2\sqrt{2}}$ $\boxed{\large\color{#20A900}answer}$

$\displaystyle \sqrt{32} + \sqrt{18} - \sqrt{50}$

$\displaystyle = \sqrt{4^2 \times 2} + \sqrt{3^2 \times 2} - \sqrt{5^2 \times 2}$

$\displaystyle = 4\sqrt{2} + 3\sqrt{2} - 5\sqrt{2}$

$\displaystyle = 2\sqrt{2}$