1. solve each equation, if possible. write irrational numbers in the simplest radical form. describe the strategy you used to get your solution and tell me why you chose it. a. 3x^2 + 27 = 0 b. x^2 - 8x + 1 = 0

A) The equation has no real roots.
B) 

Explanation
A) 3x² + 27 = 0

Subtract 27 from both sides:
3x²+27-27 = 0-27
3x² = -27

Divide both sides by 3:
3x²/3 = -27/3
x² = -9

When we go to take the square root of both sides, we will be taking the square root of a negative number; this means there are no real roots.

B) x² - 8x + 1 = 0

I chose to complete the square.  To find the value we add to both sides, take the value of b, divide by 2 and square:
(-8/2)² = (-4)² = 16
x² - 8x + 16 + 1 = 0 + 16
(x-4)² + 1 = 16

Subtract 1 from both sides:
(x-4)² + 1 - 1 = 16 - 1
(x-4)² = 15

Take the square root of both sides:
√(x-4)² = √15
x-4 = +/-√15

Add 4 to both sides:
x - 4 + 4 = 4 +/- √15
x = 4 +/- √15