Question

What is the following product

Answer 1

For this case we must find the product of the following expression:

`\sqrt [3] {5} * \sqrt {2}`

By definition of properties of powers and roots we have:

`\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}`

We rewrite the expression using the lowest common index of 6, then:

`5 ^ {\frac {1} {3}} * 2 ^ {\frac {1} {2}} =`

We rewrite the terms in an equivalent way:

`5 ^ {\frac {2} {6}} * 2 ^ {\frac {3} {6}} =`

We rewrite the expression using the property mentioned:

`\sqrt [6] {5 ^ 2} * \sqrt [6] {2 ^ 3} =`

We combine using the product rule for radicals:

`\sqrt [n] {a} * \sqrt [n] {b} = \sqrt [n] {ab}`

So:

`\sqrt [6] {5 ^ 2 * 2 ^ 3} =\\\sqrt [6] {25 * 8} =\\\sqrt[6]{200}`

ANswer:

Option b