Question
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Answer
The simplified form is \( 9u\sqrt{v} \).
Solution
To simplify √(81u²v), follow these steps:
1. Recognize that 81 and u² are perfect squares:
81 = 9² and u² = (u)².
2. Break the square root into factors:
√(81u²v) = √(81) × √(u²) × √(v).
3. Simplify the square roots of the perfect squares:
√(81) = 9 and √(u²) = u (assuming u is nonnegative).
4. Write the final simplified expression:
9u√(v).
Thus, the simplified form is 9u√(v).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To simplify \( \sqrt{81 u^{2} v} \), we can break it down into parts: \( \sqrt{81} = 9 \), \( \sqrt{u^{2}} = u \), and then we still have \( \sqrt{v} \). So, combining everything gives us \( 9u\sqrt{v} \). Now, doesn’t that just make you want to throw a little square root party? 🎉 If you're working with square roots and variables, remember that you can only take the square root of non-negative numbers. So be sure that \( v \) is non-negative to avoid any awkward moments, like when you realize your math is trying to pull off imaginary tricks!
