#(t - 9)^(1/2) - t^(1/2) = 3? #solve the radical equations, if possible.

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Answer 1 · 2017-04-13T05:16:12

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Given: #(t-9)^(1/2) - t^(1/2) = 3 " or " sqrt(t-9) - sqrt(t) = 3#

Add the #sqrt(t)# to both sides of the equation:

#sqrt(t-9) - sqrt(t) + sqrt(t) = 3 + sqrt(t)#

Simplify: #sqrt(t-9) = 3 + sqrt(t)#

Square both sides of the equation:

#(sqrt(t-9))^2 = (3 + sqrt(t))^2#

#t - 9 = (3 + sqrt(t)) ( 3 + sqrt(t))#

Distribute the right side of the equation:

#t - 9 = 9 + 3 sqrt(t) + 3 sqrt(t) + sqrt(t)sqrt(t)#

Simplify by adding like terms and using #sqrt(m) sqrt(m) = sqrt(m*m) = sqrt(m^2) = m#:

#t - 9 = 9 +6 sqrt(t) + t#

Subtract #t# from both sides:

#- 9 = 9 +6 sqrt(t)#

Subtract #-9# from both sides:

#-18 = 6 sqrt(t)#

Divide both sides by #6#:

#-3 = sqrt(t)#

Square both sides:

#(-3)^2 = (sqrt(t))^2#

#t = 9#

Check:
Always check your answer for radical problems by putting it back into the original equation to see if it works:

#sqrt(9-9) - sqrt(9) = 0 - 3 = -3 != 3#

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