Question

simplify
$\sqrt{32} - \sqrt{128} + \sqrt{200}$
​

Answer 1

• \sqrt{32}-\sqrt{128}+\sqrt{200}

=\sqrt{4×4×2}-\sqrt{4×4×4×2}+\sqrt{4×25×2}

=\sqrt{4}×\sqrt{4}×\sqrt{2} - \sqrt{4}×\sqrt{4}×\sqrt{4}×\sqrt{2} + \sqrt{4}×\sqrt{25}×\sqrt{2}

=2×2×\sqrt{2} - 2×2×2×\sqrt{2} + 2×5×\sqrt{2}

=4×\sqrt{2} - 8×\sqrt{2} + 10×\sqrt{2}

=(4-8+10)\sqrt{2}

=6×\sqrt{2}

=6\sqrt{2}