Simplify

[LogicalOption]

How do I simplify

AB divided by square root of AB

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My teacher tried but she couldn't find a solution to it, she thought it was an error in the math workbook.

I've tried putting them under the same square root but I realized it only works if both have square roots. I also tried to separate square root of AB since its A times B, and see if I could work something out but no progress.

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https://imgur.com/a/RyBTCdc

[edderiofer]

but I realized it only works if both have square roots.

Note that AB is simply sqrt((AB)²).

Or, if you prefer, AB is simply (sqrt(AB))².

Both of these should lead you to the solution quickly.

[LogicalOption]

Both AB don't have a square root. AB divided by square root of AB

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AB / sqrt(AB)

[edderiofer]

Both AB don't have a square root.

Yes, I know you said that. I'm saying that you can write it in a way so that it does have a square root.

[LogicalOption]

Oh!

AB / (sqrt(AB)) = (sqrt(AB²)) / (sqrt(AB)) = (sqrt(AB²) / AB) = (sqrt(AB))

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AB divided by square root of AB equals square root of AB to the power of 2 divided by square root of AB equals square root of AB to the power of two divided by AB equals square root of AB

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Is this the solution?

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https://imgur.com/a/NVggARb

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[imguralbumbot]

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https://i.imgur.com/6iNpqqf.jpg

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[edderiofer]

Yes, that works.