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About rationalizing denominator, is it true that you can't always multiply by the same square root denominator to get a perfect square?

  • Calculus -

    yes, because (√n)² = n

    so, multiplying the root by itself gets rid of the root.

    If the denominator is not just a root, but something like √m + n, then you need to multiply by √m - n, since

    (√m + n)(√m - n) = m - n²

    also, you sometimes have to use

    (√m + √n)(√m - √n) = m - n

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