Question

√48 + 3√27 − 7(√12 − √75)

Answer 1

Notice that:

`\begin{gathered} 48=16\cdot3=4^2\cdot3, \\ 27=9\cdot3=3^2\cdot3, \\ 12=4\cdot3=2^2\cdot3, \\ 75=25\cdot3=5^2\cdot3. \end{gathered}`

Therefore:

`\begin{gathered} \sqrt[]{48}+3\sqrt[]{27}-7(\sqrt[]{12}-\sqrt[]{75})=\sqrt[]{4^2\cdot3}+3\sqrt[]{3^2\cdot3}-7(\sqrt[]{2^2\cdot3}-\sqrt[]{5^2\cdot3}) \\ =4\sqrt[]{3}+3\cdot3\sqrt[]{3}-7(2\sqrt[]{3}-5\sqrt[]{3})\text{.} \end{gathered}`

Adding like terms we get:

`\begin{gathered} 4\sqrt[]{3}+3\cdot3\sqrt[]{3}-7(2\sqrt[]{3}-5\sqrt[]{3})=13\sqrt[]{3}-7(-3\sqrt[]{3}) \\ =13\sqrt[]{3}+21\sqrt[]{3}=34\sqrt[]{3.} \end{gathered}`

Answer: The simplified expression is:

`34\sqrt[]{3.}`