KeyionF429083 KeyionF429083
  • 25-10-2022
  • Mathematics
contestada

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

Respuesta :

LyzanderI495724 LyzanderI495724
  • 25-10-2022

[tex]-18\sqrt[]{3}[/tex]

Explanation

[tex]-27\sqrt[]{3}+3\sqrt[]{27}[/tex]

Step 1

Let's remember one propertie of the roots

[tex]\sqrt[]{a\cdot b}=\sqrt[]{a}\cdot\sqrt[]{b}[/tex]

hence

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

replacing in the expression

[tex]\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}[/tex]

therefore, the answer is

[tex]-18\sqrt[]{3}[/tex]

I hope this helps you

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