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lesya692 [45]
3 years ago
13

What is the following product

Mathematics
1 answer:
Genrish500 [490]3 years ago
4 0

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

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