How do you rationalize the denominator and simplify $sqrt 55/sqrt10$ ?

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Answer 1 · 2015-04-22T20:55:26

To keep the numbers smaller, try to reduce first. Both $55$ and $10$ are divisible by $5$ . Use that to write:

$sqrt55/sqrt10 = (sqrt5sqrt11)/(sqrt5sqrt2)= sqrt11/sqrt2$

Now rationalize tlhe denominator by multiplying by $1$ in the form: $sqrt2/sqrt2$

$sqrt55/sqrt10 = sqrt11/sqrt2 sqrt2/sqrt2 = sqrt22/2$ and we're done.

Notice

I find it worth trying to reduce first. If you don't reduce first, then you'll still get the correct answer, and it hooks like this:

$sqrt55/sqrt10 =sqrt55/sqrt10 sqrt10/sqrt10 = sqrt550/10$

$sqrt55/sqrt10 = sqrt550/10 = sqrt(55*10)/10 = sqrt(5*11*2*5)/10 = sqrt (25*22)/10 = (5sqrt22)/10 = sqrt22/2$

How do you rationalize the denominator and simplify sqrt 55/sqrt10sqrt 55/sqrt10?