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Simplify the expression 2\[sqrt(8)\ ] - 2\ [sqrt(18)\ ] - 2\ [sqrt(8)\ ].

May 11, 2026Mathematics

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Answer

-6\sqrt{2}

4 steps

Simplify each square root by factoring out perfect squares.
$\sqrt{8} = \sqrt{4 \times 2} = \sqrt{2^2 \times 2} = 2\sqrt{2}$ $\sqrt{18} = \sqrt{9 \times 2} = \sqrt{3^2 \times 2} = 3\sqrt{2}$
Substitute the simplified square roots back into the original expression.
$2\sqrt{2} - 2(3\sqrt{2}) - 2\sqrt{2}$
Perform the multiplication.
$2\sqrt{2} - 6\sqrt{2} - 2\sqrt{2}$
Combine the terms with $\sqrt{2}$ by adding or subtracting their coefficients.
$(2 - 6 - 2)\sqrt{2}$ $(-4 - 2)\sqrt{2}$ $-6\sqrt{2}$

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