For this case we must simplify the following expression:
[tex]5 \sqrt {8} - \sqrt {18} -2 \sqrt {2}[/tex]
Rewriting we have:
[tex]8 = 2 * 2 * 2 = 2 ^ 2 * 2\\18 = 9 * 2 = 3 ^ 2 * 2\\5 \sqrt {2 ^ 2 * 2} - \sqrt {3 ^ 2 * 2} -2 \sqrt {2} =[/tex]
We have that by definition of properties of roots and powers it is fulfilled:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}[/tex]
So:
[tex]5 * 2 \sqrt {2} -3 \sqrt {2} -2 \sqrt {2} =\\10 \sqrt {2} -3 \sqrt {2} -2 \sqrt {2} =\\10 \sqrt {2} -5 \sqrt {2} =\\5 \sqrt {2}[/tex]
Answer:
[tex]5 \sqrt {2}[/tex]
