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Answer
\( 6 \sqrt{80} = 24\sqrt{5} \)
Solution
To simplify 6√80, start by factoring the number inside the square root:
1. Recognize that 80 can be factored as 16 × 5.
2. Rewrite √80 as √(16×5), which equals √16 × √5.
3. Since √16 is 4, this simplifies to 4√5.
4. Now, multiply the original coefficient 6 by 4√5: 6 × 4√5 = 24√5.
The simplified expression is 24√5.
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Simplify this solution Extra Insights
To simplify \( 6 \sqrt{80} \), we can start by breaking down \( \sqrt{80} \). The number 80 can be factored into \( 16 \times 5 \). Since \( 16 \) is a perfect square, we can take it out of the square root: \[ \sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}. \] Now substitute back into the original expression: \[ 6 \sqrt{80} = 6 \times 4\sqrt{5} = 24\sqrt{5}. \] So, the simplified form of \( 6 \sqrt{80} \) is \( 24 \sqrt{5} \).
