Simplify. $$ -\sqrt{8}-3 \sqrt{18} $$ $$ \square $$

Question

UpStudy AI · Accepted Answer

We start with the expression:
$$
-\sqrt{8} - 3\sqrt{18}
$$

**Step 1:** Simplify $$\sqrt{8}$$.

Since $$8 = 4 \times 2$$ and $$4$$ is a perfect square, we have:
$$
\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}.
$$

**Step 2:** Simplify $$\sqrt{18}$$.

Similarly, since $$18 = 9 \times 2$$ and $$9$$ is a perfect square:
$$
\sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2}.
$$

**Step 3:** Substitute the simplified forms back into the original expression.

$$
-\sqrt{8} - 3\sqrt{18} = -2\sqrt{2} - 3(3\sqrt{2}) = -2\sqrt{2} - 9\sqrt{2}.
$$

**Step 4:** Combine like terms.

Since both terms contain $$\sqrt{2}$$, combine the coefficients:
$$
-2\sqrt{2} - 9\sqrt{2} = -(2+9)\sqrt{2} = -11\sqrt{2}.
$$

Thus, the simplified form is:
$$
\boxed{-11\sqrt{2}}.
$$
$$-11\sqrt{2}$$

Simplify. \( -\sqrt{8}-3 \sqrt{18} \) \( \square \)