Simplify. `(sqrt(3x^2)-3sqrt(x^2))/(3sqrt(19x^2))`Simplify the square root of 3x^2   -3 the square root of x^2 divided by 3 the square root of 19x^2. The -3 at the top is not in the square root.

Expert Answers
lemjay eNotes educator| Certified Educator


Apply the product property of radicals which is `sqrta*sqrtc=sqrt(a*c)` .

`=(sqrt3sqrt(x^2) - 3sqrt(x^2))/(3sqrt19sqrt(x^2))`

Note that `sqrt(a^2)=a` .

`=(xsqrt3 - 3x)/(3xsqrt19)`

Factor out the GCF in the numerator.


Cancel common factor between numerator and denominator.


Rationalize the denominator.


Note that `sqrt(a)*sqrt(a)=sqrt(a^2)=a` .



Hence, `(sqrt(3x^2)-3sqrt(x^2))/(3sqrt(19x^2))=(sqrt19(sqrt3-3))/57` .

embizze eNotes educator| Certified Educator

Simplify `(sqrt(3x^2)-3sqrt(x^2))/(3sqrt(19x^2))`


`=(xsqrt(3)-3x)/(3xsqrt(19))` Multiply numerator and denominator by `sqrt(19)`


which is simplified.