Question
Question Express in simplest radical form. \[ 8 \sqrt{10}-8 \sqrt{160} \]
Ask by Pope Deleon. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression simplifies to \(-24\sqrt{10}\).
Solution
Calculate or simplify the expression \( 8\sqrt{10}-8\sqrt{160} \).
Calculate the value by following steps:
- step0: Calculate:
\(8\sqrt{10}-8\sqrt{160}\)
- step1: Simplify the root:
\(8\sqrt{10}-8\times 4\sqrt{10}\)
- step2: Multiply the terms:
\(8\sqrt{10}-32\sqrt{10}\)
- step3: Collect like terms:
\(\left(8-32\right)\sqrt{10}\)
- step4: Subtract the numbers:
\(-24\sqrt{10}\)
The expression \(8\sqrt{10}-8\sqrt{160}\) simplifies to \(-24\sqrt{10}\) in simplest radical form.
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Simplify this solution The Deep Dive
To simplify the expression \( 8 \sqrt{10} - 8 \sqrt{160} \), we first simplify \( \sqrt{160} \). Noticing that \( 160 = 16 \times 10 \), we can rewrite it as follows: \[ \sqrt{160} = \sqrt{16 \times 10} = \sqrt{16} \times \sqrt{10} = 4 \sqrt{10} \] Now we can substitute this back into the expression: \[ 8 \sqrt{10} - 8 \sqrt{160} = 8 \sqrt{10} - 8(4 \sqrt{10}) = 8 \sqrt{10} - 32 \sqrt{10} \] Next, we combine like terms: \[ 8 \sqrt{10} - 32 \sqrt{10} = (8 - 32) \sqrt{10} = -24 \sqrt{10} \] Thus, the simplest radical form of the expression \( 8 \sqrt{10} - 8 \sqrt{160} \) is: \[ -24 \sqrt{10} \]
