SOLUTION: how do I solve {{{sqrt(k+9)=sqrt(3)+sqrt(k)}}}

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Question 64747This question is from textbook Algebra 2
: how do I solve
sqrt%28k%2B9%29=sqrt%283%29%2Bsqrt%28k%29 This question is from textbook Algebra 2

Answer by 303795(602) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28k%2B9%29=sqrt%283%29%2Bsqrt%28k%29
Square each side of the equation
k%2B9=3%2B2%2Asqrt%283%29%2Asqrt%28k%29%2Bk
6=2%2Asqrt%283%29%2Asqrt%28k%29
Divide each side by 2
3=sqrt%283%29%2Asqrt%28k%29
Divide each side by sqrt(3)
sqrt%283%29=sqrt%28k%29
Square each side to get
3=k
Check in the original equation
sqrt%283%2B9%29=sqrt%283%29%2Bsqrt%283%29
sqrt%2812%29=2sqrt%283%29
sqrt%284%2A3%29=2sqrt%283%29
2sqrt%283%29=2sqrt%283%29