How do you solve #5+sqrt(g-3)=6# and check your solution?

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Answer 1 · 2017-07-06T05:57:32

#g=4#

#5+sqrt(g-3)=6#

Subtract #5# from each side.

#5-5+sqrt(g-3)=6-5#

#sqrt(g-3)=1#

Square both sides.

#g-3=1^2#

Since the square of #1# is #1#:

#g-3=1#

Add #3# to each side.

#g-3+3=1+3#

#g=4#

To check substitute #g# with #4# in the original equation:

#5+sqrt(g-3)=6#

#5+sqrt(4-3)=6#

#5+sqrt1=6#

The square root of #1# is either #+1# or #-1#. Taking it to be #+1#:

#5+1=6#

We can use slightly different steps for the last two steps to confirm the solution:

#5+sqrt1=6#

Subtract #5# from each side.

#5-5+sqrt1=6-5#

#sqrt1=1#

Square both sides. The square of #1# is #1#.

#1=1#