Principle of Square Roots

For any nonnegative real number k, if x 2 = k, then x = or x =. -

x x 2 = 9 3 = like x 2 – 9 = 0 (x + 3)(x – 3) = 0 {± 3 } x 2 = 9

x x 2 = = like x 2 – 100 = 0 (x + 10)(x – 10) = 0 {± 10 } x 2 = 100

x x 2 = = like x 2 – 14 = 0 (x + )(x – ) = 0 Can’t factor. Answers are not rational. x 2 = 14

x x 2 = = x 2 = 29 like x 2 – 29 = 0 (x + )(x – ) = 0 Can’t factor. Answers are not rational.

x x 2 = -1 i = like x = 0 (x )(x ) = 0 Can’t factor. Answers are not rational.

x x 2 = -16 4i4i =

x x 2 = = 9x 2 = 25 x = 25 9

x x 2 = = 16x 2 = 49 x = 49 16

x x 2 = = 9x 2 = 13 x =

x x 2 = = 16x 2 = 41 x =

x x 2 = = 3x 2 = 2 x =

x x 2 = = 5x 2 = 11 x =

x x 2 = 8 8 = x = 2·2·2 x =22

x x 2 = = x 2 = 12 x = 2·2·3 x = 23

x x 2 = = x 2 = 32 x = 2·2·2·2·2 x = 4 22·22 x =

x x 2 = = x 2 = -20 x = -2·2·5 x = 2i2i5

x x 2 = = x 2 = -24 x = -2·2·6 x= 2i2i6 -2·2·2·3

x x 2 = 0 0 = x = 0 dr

x x 2 = = 7x 2 = 32 x = x = x = Wow!

x x 2 = = 18x 2 = -1 x = x = x = Double wow!

That’s all!