Question

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

Answer 1

Steps:

So firstly, add both sides by 27:

`(v-2)^2=27`

Next, square root both sides of the equation:

`v-2=\pm √(27)`

Now, we are going to simplify the radical. To do this, we will apply the product rule of radicals which states that
`√(ab)=√(a)*√(b)` . In this case:

`√(27)=√(9)*√(3)=3√(3)\\\\v-2=\pm\ 3√(3)`

Lastly, add both sides by 2:

`v=2\pm 3√(3)`

Answer:

In exact form, your answer is
`v=2\pm 3√(3)`

Answer 2

v = 2 ± 3 sqrt(3)

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)