Score: $$ 9 / 10 $$ Penalty: none Question Express in simplest radical form. $$ -10 \sqrt{5}+\sqrt{80} $$

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UpStudy AI · Accepted Answer

We start with the expression:
$$
-10 \sqrt{5} + \sqrt{80}
$$

**Step 1: Simplify $$\sqrt{80}$$**

Notice that:
$$
80 = 16 \times 5
$$
So,
$$
\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \cdot \sqrt{5} = 4\sqrt{5}
$$

**Step 2: Combine like terms**

Substitute the simplified $$\sqrt{80}$$ back into the expression:
$$
-10\sqrt{5} + 4\sqrt{5}
$$
Since both terms contain $$\sqrt{5}$$, combine the coefficients:
$$
(-10 + 4)\sqrt{5} = -6\sqrt{5}
$$

Thus, the expression in simplest radical form is:
$$
-6\sqrt{5}
$$
The expression simplifies to $$-6\sqrt{5}$$.

Score: \( 9 / 10 \) Penalty: none Question Express in simplest radical form. \[ -10 \sqrt{5}+\sqrt{80} \]

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