Solving Radical Equations

Question

Solve and Check: (√t−14) = 4



Enter any solution as an integer or reduced fraction. Separate with commas if there is more than one solution. If there are no solutions, click the No Solution button.

Answer 1

sqr(t) - 14 = 4

add 14 to both sides to get:

sqr(t) = 18

square both sides:

t = 18^2

t = 324

UNLESS you really meant

sqr(t-14) = 4

then square both sides to get:

t-14 = 4^2 = 16

then add 14 to both sides

t = 16+14 =30

t = 30

slight difference

the use of ( ) around sqrt -14 is not conclusive, but

they do suggest you probably want the 2nd answer, t=30

yet technically, the problem as written would require the 1st: t= 324

this also all assumes you mean sqr(t) as only the positive square root

while it makes no difference in this problem, it is wise to check the answer(s)

and plug them back into the original equation.

sometimes you can introduce an extraneous solution that isn't in the original problem

whenever you multiply by a term that has a variable, such as squaring both sides

and one side has a variable in it

sqr(30-14) =sqr16 = 4

or

sqr(324)-14 = 18-14= 4

not a problem in this problem