Exploring Square Root Functions and Equations

A solution that is always positive

A solution that does not satisfy the original equation

A solution that satisfies the original equation

A solution that is always negative

Get the square root by itself

Subtract the constant term

Check for extraneous roots

Square both sides of the equation

x = 4

x = 2

x = 0

x = 1

Because the equation has a negative square root

Because the square root expression is not isolated

Because the equation is quadratic

Because the solution is extraneous

x = 7 and x = -6

x = -7 and x = 6

x = 6 and x = 7

x = -6 and x = -7

x = 4

x = -4

x = -2

x = 2

Check for extraneous roots

Set the expression under the radical greater than or equal to zero

Square both sides of the inequality

Subtract the constant term

x is between -2 and 25

x is between 2 and -25

x is between -2 and -25

x is between 2 and 25

b is greater than 12

b is greater than 43

b is greater than 36

b is greater than 7

Because the inequality is quadratic

Because the square root expression is not isolated

Because the inequality produces an untrue statement

Because the solution is extraneous