Respuesta :

factor took out was [tex]y^2[/tex] , And resultant expression is  [tex]y\sqrt{3}[/tex] .

Step-by-step explanation:

Here we need to Take a factor out of the square root:  sqrt(3y^2) , where y<0 .Let's do this :

The given expression is  sqrt(3y^2) or , [tex]\sqrt{(3y^2)}[/tex]

We know that , to take out a factor out of the square root that factor must have a degree in multiple of 2 , as   [tex]x^2,x^4,x^16,(x+6)^2,(x-2)^4[/tex]  etc . So ,

[tex]\sqrt{3y^2}[/tex]

⇒ [tex]\sqrt{3}(\sqrt{y^2})[/tex]

⇒ [tex]\sqrt{3}(y^2)^{\frac{1}{2}[/tex]

⇒ [tex]\sqrt{3}(y)^{\frac{2}{2}[/tex]

⇒ [tex]y\sqrt{3}[/tex]

Therefore , factor took out was [tex]y^2[/tex] , And resultant expression is  [tex]y\sqrt{3}[/tex] .

Answer:

-y × sqrt(3)

Step-by-step explanation:

3y²

3 × (-y)²

sqrt(3 × (-y)²)

-y × sqrt(3)

y < 0

-y > 0

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