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ahoymewmew Group Title

Can someone help me with Multiplying Radicals?

  • 2 years ago
  • 2 years ago

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  1. ahoymewmew Group Title
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    These are the problems. V

    • 2 years ago
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  2. wio Group Title
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    Where are you stuck? Do you know: \[\sqrt{a}\times \sqrt{b} = \sqrt{a\times b}\]

    • 2 years ago
  3. ahoymewmew Group Title
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    no @wio its confusing me.

    • 2 years ago
  4. CliffSedge Group Title
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    Multiply the numbers that are outside the radicals together, then multiply the numbers inside the radicals together. If the new radicand can be simplified by extracting roots, then do that and multiply those roots by the numbers outside.

    • 2 years ago
  5. CliffSedge Group Title
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    #3 as an example: \[7xy \sqrt{2x} \cdot 3\sqrt{4xy^2} \rightarrow (7xy)(3) \cdot \sqrt{(2x)(4xy^2)}\]

    • 2 years ago
  6. CliffSedge Group Title
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    \[(7xy)(3) \cdot \sqrt{(2x)(4xy^2)} = 21xy \cdot \sqrt{2 \cdot 4 \cdot x^2 \cdot y^2}\] The radical contains the squares, 4, x^2, and y^2, so take the roots of those out. \[21xy \cdot 2 \cdot x \cdot y \sqrt{2}\] Then just simplify that the rest of the way.

    • 2 years ago
  7. CliffSedge Group Title
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    Also note that you could have simplified the second radical first by taking out the 2 and the y since it had 4y^2 as a perfect square already.

    • 2 years ago
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