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Ayna and Leslie both simplified the expression.What was the mistake made by the student that was incorrect. Explain your reasoning

Ayna and Leslie both simplified the expression.What was the mistake made by the student-example-1
User Mackristo
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1 Answer

5 votes

The Solution:

The given expression is


\sqrt[]{18x^4y^5}
\begin{gathered} \sqrt[]{18x^4y^5}=\text{ }\sqrt[]{2(3)(3)(x)(x)(x)(x)(y)(y)(y)(y)(y)} \\ \\ \sqrt[]{18x^4y^5}=\text{ }\sqrt[]{2(3^2)(x^2)(x^2)(y^2)(y^2)(y)}=3x^2y^2\text{ }\sqrt[]{2y} \end{gathered}

Clearly, we have that Ayna's work was wrong.


\begin{gathered} \text{ Ayna wrote} \\ 2x^2y^2\sqrt[]{3x^2y}\text{ instead of} \\ \\ 3x^2y^2\sqrt[]{2y} \end{gathered}

But Lesile' work is correct.

Thus, the correct answer is


3x^2y^2\text{ }\sqrt[]{2y}

User Jesu
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