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LiRa [457]
3 years ago
5

Multiply.

Mathematics
1 answer:
Nady [450]3 years ago
3 0

\boxed{3\sqrt{22}\sqrt{58}\sqrt{18}=18\sqrt{638}}

<h2>Explanation:</h2>

Here we have the following expression:

3\sqrt{22}\sqrt{58}\sqrt{18}

So we need to simplify that radical expression. By property of radicals we know that:

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

So:

3\sqrt{22}\sqrt{58}\sqrt{18}=3\sqrt{22\times 58 \times 18}=3\sqrt{22968}

The prime factorization of 22968 is:

22968=2^3\cdot 3^2\cdot11\cdot 29

Hence:

3\sqrt{22968}=3\sqrt{2^3\cdot 3^2\cdot11\cdot 29}=3\sqrt{2^2\cdot 3^2\cdot 2\cdot 11\cdot 29}

By property:

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

So:

3\sqrt{2^2\cdot 3^2\cdot 2\cdot 11\cdot 29} \\ \\ 3(2)(3)\sqrt{2\cdot 11\cdot 29}=18\sqrt{638}

Finally:

\boxed{3\sqrt{22}\sqrt{58}\sqrt{18}=18\sqrt{638}}

<h2>Learn more:</h2>

Radical expressions: brainly.com/question/13452541

#LearnWithBrainly

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