Respuesta :

wegnerkolmp2741o

Answer:

v = 2 ± 3 sqrt(3)

Step-by-step explanation:

(v-2)^2-27=0

add 27 to each side

(v-2)^2-27+27=0+27

(v-2)^2 = 27

take the square root of each side , remember to take the  positive and negative

sqrt((v-2)^2)   = ± sqrt27

v-2 =  ± sqrt27

add 2 to each side

v-2+2 = 2 ± sqrt27

v = 2 ± sqrt27

we can simplify the square root of 27

sqrt(27) = sqrt(9) * sqrt(3)

sqrt(27) = 3sqrt(3)

v = 2 ± 3 sqrt(3)


GoddessofDork

Steps:

So firstly, add both sides by 27:

[tex](v-2)^2=27[/tex]

Next, square root both sides of the equation:

[tex]v-2=\pm \sqrt{27}[/tex]

Now, we are going to simplify the radical. To do this, we will apply the product rule of radicals which states that [tex]\sqrt{ab}=\sqrt{a}*\sqrt{b}[/tex] . In this case:

[tex]\sqrt{27}=\sqrt{9}*\sqrt{3}=3\sqrt{3}\\\\v-2=\pm\ 3\sqrt{3}[/tex]

Lastly, add both sides by 2:

[tex]v=2\pm 3\sqrt{3}[/tex]

Answer:

In exact form, your answer is [tex]v=2\pm 3\sqrt{3}[/tex]

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