Question

3√12-√32+√27+2√8 simplified

Answer 1

`9\sqrt[]{3}`Step-by-step explanation:
`3\surd12-\surd32+\surd27+2\surd8`

We check if the numbers in under square root can be broken down into numbers we can find the square root:

`\begin{gathered} 12\text{ = 4}*3 \\ 32\text{ = 2 }*16 \\ 27\text{ = 3}*9 \\ 8\text{ = 2}*4 \end{gathered}`
`\begin{gathered} 3\surd(4*3)-\surd(2*16)+\surd(3*9)+2\surd(2*4) \\ 3*\surd(4*3)-\surd(2*16)+\surd(3*9)+2*\surd(2*4) \\ 3*2\sqrt[]{3}\text{ - 4}\sqrt[]{2}\text{ + 3}\sqrt[]{3}\text{ + 2}*2\sqrt[]{2} \end{gathered}`
`\begin{gathered} 6\sqrt[]{3}\text{ -4}\sqrt[]{2}\text{ + 3}\sqrt[]{3}\text{ + 4}\sqrt[]{2} \\ 9\sqrt[]{3}\text{ -4}\sqrt[]{2}\text{ +4}\sqrt[]{2} \end{gathered}`
`\begin{gathered} =\text{ 9}\sqrt[]{3}\text{ + 0} \\ =\text{ 9}\sqrt[]{3} \end{gathered}`