Question

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

Answer 1

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)

Answer 2

Steps:

So firstly, add both sides by 27:

$(v-2)^2=27$

Next, square root both sides of the equation:

$v-2=\pm \sqrt{27}$

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

$\sqrt{27}=\sqrt{9}*\sqrt{3}=3\sqrt{3}\\\\v-2=\pm\ 3\sqrt{3}$

Lastly, add both sides by 2:

$v=2\pm 3\sqrt{3}$

Answer:

In exact form, your answer is $v=2\pm 3\sqrt{3}$