Question

Simplify square root if 2 times the cubed root of 2

Answer 1

The exponent rule states that
`a^(b) × a^(c) = a^(b+c)`.


`\sqrt[2]{2}~*~ \sqrt[3]{2}` is equivalent to
`2^{(1)/(2) }~*~2^{(1)/(3) }`.

You keep the coefficients the same, but add together the exponents.


`(1)/(2)~+~(1)/(3)~=~(3)/(6)~+~(2)/(6)~=~(5)/(6)`



`2^{ (5)/(6)}`
OR

`\sqrt[6]{2^(5)}`
OR

`\sqrt[6]{32}`.

Answer 2

To simplify this, you need to apply the exponent rule;
`a^(b) * a^(c) = a^(b + c)`.

Your answer should be
`2^(5/6)`.
Hope this helped!