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.

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lemjay | High School Teacher | (Level 3) Senior Educator

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

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.

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

Cancel common factor between numerator and denominator.

`=(sqrt3-3)/(3sqrt19)`

Rationalize the denominator.

`=(sqrt3-3)/(3sqrt19)*(sqrt19)/(sqrt19)`

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

`=(sqrt19(sqrt3-3)/(3*19)`

`=(sqrt19(sqrt3-3))/57`

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

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embizze | High School Teacher | (Level 1) Educator Emeritus

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

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

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

`=(sqrt(19)(xsqrt(3)-3x))/(57x)`

which is simplified.

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