How do you solve these equations?

Question

Square root of (x-1)^2 = the square root of 3

Answer 1

((x-1)^2)^(1/2) = 3^(1/2)
x-1 = 3^(1/2)
x = 1+ 3^(1/2)

When you take the square root of a perfect square, you get the root.

Answer 2

Square root of (x-1)^2 = the square root of 3
sqrt(A) = sqrt(B) <=> A = B and A >= 0 or B >=0
thus
<=> (x-1)^2 = 3
<=> x^2 -2x - 2 =0
<=> x = 1 + sqrt(3) or x = 1 - sqrt(3)

Answer 3

Clear the square root from both sides. Presuming that the entire expression (x-1)^2 is under the root sign, your equation becomes:

(x-1)^2 = 3

then

x^2-2x+1 = 3
x^2-2x-2 = 0

Use the quadratic equation to solve, which should give you two solutions: 1 + (sq.rt.12)/2 and 1 - (sq.rt. 12)/2

Answer 4

sqrt[(x-1)^2] = sqrt[3]

the square root of a squared value is simply the value itself, so:
(x-1) = sqrt[3]

which means:
x = sqrt[3] + 1

x= 1.732 + 1

therefore:
x = 2.732

Answer 5

wHAT DOES ^ 2 MEAN?