How do you rationalize the denominator and simplify $sqrt33 /sqrt77$ ?

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Answer 1 · 2015-04-13T10:14:41

Before we rationalise the denominator, let's simplify the fraction.

$sqrt33 /sqrt77$

$= sqrt(3*11)/sqrt(7*11)$

$= (sqrt3*cancel(sqrt11))/(sqrt7*cancel(sqrt11))$

$= sqrt 3 / sqrt 7$

Now we can rationalise the denomintor by multiplying the numerator as well as the denominator by $sqrt 7$

$= sqrt 3 / sqrt 7 * color(blue)(sqrt 7/ sqrt 7$
(We are multiplying $sqrt 3 / sqrt 7$ with $color(blue)1$ )

$= (sqrt 3 * sqrt 7) / 7$

$= (sqrt (3 * 7)) / 7$ (In general $sqrta*sqrtb = sqrt(ab)$ )

$color(green)( = (sqrt 21) / 7$

As the denominator 7 is Rational, we can say that we have Rationalised the denominator of the original fraction $sqrt33 /sqrt77$

How do you rationalize the denominator and simplify sqrt33 /sqrt77sqrt33 /sqrt77?