Question 118061
#1


{{{sqrt(5/3)}}} Start with the given expression



{{{sqrt(5)/sqrt(3)}}} Break up the square root



{{{(sqrt(5)/sqrt(3))(sqrt(3)/sqrt(3))}}} Multiply the fraction by {{{sqrt(3)/sqrt(3)}}}



{{{(sqrt(5)sqrt(3))/(sqrt(3)sqrt(3))}}} Combine the fraction



{{{(sqrt(5*3))/(sqrt(3*3))}}} Combine the roots



{{{sqrt(15)/sqrt(9)}}} Multiply



{{{sqrt(15)/3}}} Take the square root of 9 to get 3. Notice how the denominator is a rational number. This is why I multiplied the fraction by {{{sqrt(3)/sqrt(3)}}}




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#2



{{{sqrt(12x^3/5)}}} Start with the given expression



{{{sqrt(12x^3)/sqrt(5)}}} Break up the square root



{{{(sqrt(12x^3)/sqrt(5))(sqrt(5)/sqrt(5))}}} Multiply the fraction by {{{sqrt(5)/sqrt(5)}}}



{{{(sqrt(12x^3)sqrt(5))/(sqrt(5)sqrt(5))}}} Combine the fraction



{{{(sqrt(12x^3*5))/(sqrt(5*5))}}} Combine the roots



{{{sqrt(60x^3)/sqrt(25)}}} Multiply



{{{sqrt(60x^3)/5}}} Take the square root of 25 to get 5. 



{{{sqrt(4*15x^2*x)/5}}} Factor 60 into 4*15 {{{x^3}}} into {{{x^2*x}}}



{{{sqrt(4)sqrt(15)sqrt(x^2)sqrt(x)/5}}} Break up the root



{{{(2sqrt(15)x*sqrt(x))/5}}} Take the square root of {{{4}}} to get 2 and take the square root of {{{x^2}}} to get x


{{{(2*x*sqrt(15)sqrt(x))/5}}} Rearrange the terms



{{{(2x*sqrt(15x))/5}}} Combine the roots


So {{{sqrt(12x^3/5)}}} simplifies to {{{(2x*sqrt(15x))/5}}}