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#