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I'm confused with what would happen after multiplying something with its conjugate.

For example, what would $\sqrt{(4+x^2)}$ multiplied by its conjugate $\sqrt{(4-x^2)}$ be?

$(4+x^2)^{\frac12}\times(4-x^2)^{\frac12} = ?$ Would the square root stay or leave?

I know this is a basic question. Please bear with me. Thank you so much!

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    $\begingroup$ The nice thing about roots is $\sqrt{a}\sqrt{b} = \sqrt{ab}$. So you can combine the roots, then use the third binomial theorem. $\endgroup$
    – Anon
    Commented Jun 22, 2016 at 6:13

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We have

$$\left( \sqrt{4 + x^2} \right) \left( \sqrt{4 - x^2} \right) = \sqrt{(4+x^2)(4-x^2)}=\sqrt{16-x^4}.$$

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