SOLUTION: What is the answer to the equation square root of y + the square root of (y+5) = 5 or √y + √(y+5) = 5

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Question 710988: What is the answer to the equation square root of y + the square root of (y+5) = 5 or √y + √(y+5) = 5
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
Solve by squaring your equation
(1) sqrt%28y%29 + sqrt%28y+%2B+5%29 = 5 and get
(2) y + 2*sqrt%28y%29*sqrt%28y%2B5%29 + (y+5) = 25 or
(3) sqrt%28y%29*sqrt%28y%2B5%29 = 10 - y
Now square (3) to get
(4) y*(y + 5) = 100 -20y + y%5E2 or
(5) y%5E2 + 5y = y%5E2 -20y + 100 or
(6) 5y = -20y + 100 or
(7) 25y = 100 or
(8) y = 4
Let's check your answer in (1)
Is (sqrt%284%29 + sqrt%284+%2B+5%29 = 5)?
Is (2 + sqrt%289%29 = 5)?
Is (2 + 3 = 5)?
Is (5 = 5)? Yes
Answer: y = 4