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A) Describe the two errors in the students work simplifying the radical expression B) correctly simplify the radical expression

A) Describe the two errors in the students work simplifying the radical expression-example-1
User Deuce
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A) Describe the two errors in the students work simplifying the radical expression

The first thing we have to do is take the factors of the number


\begin{gathered} \sqrt[3]{108\cdot a^(11)\cdot b^(14)\cdot c^5} \\ 108=2^2\cdot3^3 \\ \sqrt[3]{2^2\cdot3^3\cdot a^(11)\cdot b^(14)\cdot c^5} \end{gathered}

• The first error is the factors of 108 missing to square the 2

Now we decompose each of the variables into factors of 3:


\begin{gathered} a^(11)=a^3\cdot a^3\cdot a^3\cdot a^2=(a^3)^3\cdot a^2=a^9\cdot a^2 \\ b^(14)=b^3\cdot b^3\cdot b^3\cdot b^3\cdot b^2=(b^3)^4\cdot b^2=b^(12)\cdot b^2 \\ c^5=c^3\cdot c^2 \end{gathered}

We add the factors within the cubic root


\sqrt[3]{2^2\cdot3^3\cdot a^9\cdot a^2\cdot b^(12)\cdot b^2\cdot c^3\cdot c^2^{}}

• The second error is the factors of the variable b because raised to 14 is b^12+ b^2 squared not b^9 +b^2

To finish we solve by taking all the factors cubed:


\begin{gathered} \sqrt[3]{2^2\cdot3^3\cdot a^9\cdot a^2\cdot b^(12)\cdot b^2\cdot c^3\cdot c^2} \\ 3\cdot a^3\cdot b^4\cdot c\cdot\sqrt[3]{2^2\cdot a^2\cdot b^2\cdot c^2} \\ 3\cdot a^3\cdot b^4\cdot c\cdot\sqrt[3]{4^{}\cdot a^2\cdot b^2\cdot c^2} \end{gathered}

So the answer is


3\cdot a^3\cdot b^4\cdot c\cdot\sqrt[3]{4^{}\cdot a^2\cdot b^2\cdot c^2}

User Bogdan Vakulenko
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