Question

-27\sqrt(3)+3\sqrt(27), reduce the expression

Answer 1

`-18\sqrt[]{3}`

Step-by-step explanation

`-27\sqrt[]{3}+3\sqrt[]{27}`

Step 1

Let's remember one propertie of the roots

`\sqrt[]{a\cdot b}=\sqrt[]{a}\cdot\sqrt[]{b}`

hence

`\sqrt[]{27}=\sqrt[]{9\cdot3}=\sqrt[]{9}\cdot\sqrt[]{3}=3\sqrt[]{3}`

replacing in the expression

`\begin{gathered} -27\sqrt[]{3}+3\sqrt[]{27} \\ -27\sqrt[]{3}+3(3\sqrt[]{3}) \\ -27\sqrt[]{3}+9\sqrt[]{3} \\ (-27+9)\sqrt[]{3} \\ -18\sqrt[]{3} \end{gathered}`

therefore, the answer is

`-18\sqrt[]{3}`

I hope this helps you