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svlad2 [7]
3 years ago
8

Which of the following is equivalent to 5 square root 13^3

Mathematics
1 answer:
igor_vitrenko [27]3 years ago
7 0

For this case we must find an expression equivalent to the following:

5 \sqrt {13 ^ 3}

By definition of properties of powers and roots we have:

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

In addition, we know that:

13 ^ 3 = 13 ^ 2 * 13

Rewriting the given expression we have:

5 \sqrt {13 ^ 3} = 5 \sqrt {13 ^ 2 * 13} = 13 * 5 \sqrt {13} = 65 \sqrt {13}

Answer:

65 \sqrt {13}

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