How do you rationalize the denominator and simplify sqrt (33/77)?

1 Answer
Johnson Z.
Mar 15, 2016

sqrt(21)/7

Explanation:

1. Since the denominator of the fraction contains a radical, start by multiplying the numerator and denominator by sqrt(77)/sqrt(77). Note that sqrt(77)/sqrt(77)=1, so that value of the fraction remains the same.

sqrt(33)/sqrt(77)

=sqrt(33)/sqrt(77)(sqrt(77)/sqrt(77))

2. Simplify.

=sqrt(33*77)/77

=sqrt(2541)/77

3. Use a perfect square to break down the radical in the numerator.

=sqrt(11^2*21)/77

4. Simplify.

=(11sqrt(21))/77

=(color(red)cancelcolor(black)11^1sqrt(21))/color(red)cancelcolor(black)77^7

=color(green)(|bar(ul(color(white)(a/a)sqrt(21)/7color(white)(a/a)|)))

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