In most cases, a square root in an equation can be eliminated by squaring. However, this method can sometimes produce solutions that don't work named extraneous roots, so all solutions need to be verified.
If the equation has two or more roots, the squaring process can be repeated for each of them.


Example:
Find the solutions of the following equation:





Both x = 0 and x = -1 check in the original equation.


Find the solutions of the following equations:


1:



x = 0

x = 2 and x = -2

x = 2 and x = -3

x = 2




2:



x = 4

x = 4 and x = -3

x = 4, x = -4 and x = -3

x = 28



3:



x = 1

x = 16

x = 4

x = 3




4:



x = 2

x = -4

x = 0

x = 4




5:



x = -2 and x = 7

x = -2

x = 7

x = 2 and x = 4



6:



x = 0, x = -2 and x = 2

x = 0, x = -4 and x = 4

x = -4 and x = 4

x = 0 and x = 4



7:



x = 12

x = -1

x = 15

x = 1



8:



x = 4

x = -3

x = 5/3

x = 25/9





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