Solve (v-2)^2-27=0 where v is a real number. simplify your answer as much as possible

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)

So firstly, add both sides by 27:

Next, square root both sides of the equation:

Now, we are going to simplify the radical. To do this, we will apply the product rule of radicals which states that . In this case:

Lastly, add both sides by 2:

In exact form, your answer is

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step-by-step explanation:

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