Question

How do you rationalize the denominator and simplify `4/sqrt2`?

Answer 1

`2sqrt2`

Explanation:

Multiply by 1 but in the form of `1=sqrt(2)/sqrt(2)`

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`color(blue)("Comment")`

Multiplying by 1 does not change the inherent value.
So multiplying by `1=sqrt2/sqrt2` changes the way it looks without changing its inherent value.
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`4/sqrt2xxsqrt2/sqrt2" " =" " (cancel(4)^2sqrt2)/(cancel(2)^1)`

`=2sqrt2`