How do you rationalize the denominator and simplify sqrt21/sqrt6?

1 Answer
Johnson Z.
Mar 15, 2016

sqrt(106)/6

Explanation:

1. Since the denominator of the fraction contains a radical, start by multiplying the numerator and denominator by sqrt(6)/sqrt(6). Note that sqrt(6)/sqrt(6)=1, so that value of the fraction remains the same.

sqrt(21)/sqrt(6)

=sqrt(21)/sqrt(6)(sqrt(6)/sqrt(6))

2. Simplify.

=sqrt(21*6)/6

=color(green)(|bar(ul(color(white)(a/a)sqrt(106)/6color(white)(a/a)|)))

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