#sqrt (t) = sqrt (t - 12) + 2? #solve the radical equations, of possible.

2 Answers
Apr 16, 2017

Answer:

THIS ANSWER IS INCORRECT. SEE THE CORRECT SOLUTION ABOVE.

Explanation:

Start by squaring both sides to get rid of one of the radicals, then simplify and combine like terms.
#sqrtt^color(green)2=(sqrt(t-12)+2)^color(green)2#
#t=t-12+4sqrt(t-12)+4#
#t=t-8+4sqrt(t-12)#

Then operate on both sides of the equation to isolate the other radical.
#tcolor(green)(-t)=color(red)cancelcolor(black)t-8+4sqrt(t-12)color(red)cancelcolor(green)(-t)#
#0color(green)(+8)=color(red)cancelcolor(black)("-"8)+4sqrt(t-12)color(red)cancelcolor(green)(+8)#
#color(green)(color(black)8/4)=color(green)((color(red)cancelcolor(black)4color(black)sqrt(t-12))/color(red)cancelcolor(green)4#
#8=sqrt(t-12)#

And square both sides again to get rid of the other radical.
#8^color(green)2=sqrt(t-12)^color(green)2#
#64=t-12#

Finally, add #12# to both sides to isolate #t#.
#64color(green)(+12)=tcolor(red)cancelcolor(black)(-12)color(red)cancelcolor(green)(+12)#
#76=t#
#t=76#

When working with radicals, always check your solutions to make sure they aren't extraneous (make sure they don't cause there to be a square root of a negative number). In this case both #76# and #76-12# are positive, so #76# is a valid solution for #t#.

Apr 17, 2017

Answer:

#x in {16}#

Explanation:

Rearrange the equation:

#sqrt(t) - 2 = sqrt(t - 12)#

Square both sides:

#(sqrt(t) - 2)^2 = (sqrt(t - 12))^2#

#t - 4sqrt(t) + 4 = t - 12#

Simplify:

#16 = 4sqrt(t)#

#4 = sqrt(t)#

Square both sides once more.

#16 = t#

Check the solution is accurate.

#sqrt(16) = sqrt(16 - 12) + 2 -> 4 = 4 color(green)(√)#

Hopefully this helps!