How do you simplify sqrt45/(4sqrt81)?

1 Answer
Johnson Z.
Mar 15, 2016

sqrt(5)/12

Explanation:

1. Start by multiplying the numerator and denominator by sqrt(81)/sqrt(81) to get rid of the radical in the denominator. Note that the value of the fraction would not change since sqrt(81)/sqrt(81)=1.

sqrt(45)/(4sqrt(81))

=sqrt(45)/(4sqrt(81))(sqrt(81)/sqrt(81))

2. Simplify.

=sqrt(45*81)/(4(sqrt(81)sqrt(81)))

=sqrt(3645)/(4(81))

=sqrt(3645)/324

3. Using a perfect square, break down the radical in the numerator.

=sqrt(27^2*5)/324

4. Simplify.

=(27sqrt(5))/324

=(color(red)cancelcolor(black)27^1sqrt(5))/color(red)cancelcolor(black)324^12

=color(green)(|bar(ul(color(white)(a/a)sqrt(5)/12color(white)(a/a)|)))

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