Question

Please help! Rewrite the radical as a rational exponent. 3√2 7

Answer 1

For this case we have:

By property of the radicals: $\sqrt {n} = n ^ {\frac {1} {2}}$

Given $3 \sqrt {27}$

We can rewrite it as:

$3 \sqrt {(3 * 3 * 3)} =\\3 \sqrt {(3 ^ 2 * 3)}$

We know that by property of the radicals:

$\sqrt {n * m} = \sqrt {n} * \sqrt {m}$, then:

$3 \sqrt {(3 ^ 2 * 3)} = 3 (\sqrt {3 ^ 2} *\sqrt {3})$

Simplifying, considering that $\sqrt {9} = 3$, we have:

$3 * 3 * \sqrt {3} =\\9 \sqrt {3} =\\9 * (3) ^ {\frac {1} {2}}$

Answer:

$3 \sqrt {27} = 9 * (3) ^ {\frac {1} {2}}$