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}}`