Answer: [tex]6\sqrt[]{3}-2\sqrt[]{5}-3\sqrt[]{2}[/tex]
Step-by-step explanation:
[tex]\sqrt[]{108}+\sqrt[]{80}-\sqrt[]{180}-\sqrt[]{18}[/tex]
Let's solve each square root separately.
[tex]\sqrt[]{108} =\sqrt[]{6^2} *\sqrt[]{3} =6\sqrt[]{3}[/tex]
[tex]\sqrt[]{80}=\sqrt[]{10} *\sqrt[]{8}=\sqrt[]{10}*\sqrt[]{2^2*2} =2\sqrt[]{10*2} =2\sqrt[]{20}=2\sqrt[]{2^2*5} =2*2\sqrt[]{5}=4\sqrt[]{5}[/tex]
[tex]\sqrt[]{180}=\sqrt[]{2^2}*\sqrt[]{5} *\sqrt[]{3^2} =2*3\sqrt[]{5}=6\sqrt[]{5}[/tex]
[tex]\sqrt[]{18}=\sqrt[]{3^2}*\sqrt[]{2}=3\sqrt[]{2}[/tex]
Now let's use the new information.
[tex]6\sqrt[]{3}+4\sqrt[]{5} -6\sqrt[]{5} -3\sqrt[]{2}[/tex]
Add or subtract those square root whose numbers are equal.
[tex]6\sqrt[]{3}-2\sqrt[]{5}-3\sqrt[]{2}[/tex]
