For this case we have:
By property of the radicals: [tex]\sqrt {n} = n ^ {\frac {1} {2}}[/tex]
Given [tex]3 \sqrt {27}[/tex]
We can rewrite it as:
[tex]3 \sqrt {(3 * 3 * 3)} =\\3 \sqrt {(3 ^ 2 * 3)}[/tex]
We know that by property of the radicals:
[tex]\sqrt {n * m} = \sqrt {n} * \sqrt {m}[/tex], then:
[tex]3 \sqrt {(3 ^ 2 * 3)} = 3 (\sqrt {3 ^ 2} *\sqrt {3})[/tex]
Simplifying, considering that [tex]\sqrt {9} = 3[/tex], we have:
[tex]3 * 3 * \sqrt {3} =\\9 \sqrt {3} =\\9 * (3) ^ {\frac {1} {2}}[/tex]
Answer:
[tex]3 \sqrt {27} = 9 * (3) ^ {\frac {1} {2}}[/tex]
