Question
Score: \( 9 / 10 \) Penalty: none Question Express in simplest radical form. \[ -10 \sqrt{5}+\sqrt{80} \]
Ask by Johnson Collins. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression simplifies to \(-6\sqrt{5}\).
Solution
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:
\[
-6\sqrt{5}
\]
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Simplify this solution Mind Expander
To express \(-10 \sqrt{5} + \sqrt{80}\) in simplest radical form, we first simplify \(\sqrt{80}\). Notice that: \[ \sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \cdot \sqrt{5} = 4\sqrt{5} \] Now, we can substitute this back into the expression: \[ -10 \sqrt{5} + \sqrt{80} = -10 \sqrt{5} + 4 \sqrt{5} \] Next, combine the like terms: \[ (-10 + 4) \sqrt{5} = -6 \sqrt{5} \] Thus, the expression in simplest radical form is: \[ -6 \sqrt{5} \]
