Please help me simplify

Question

Please help me simplify:

 

√y + (√y + 7) = 7

 

Inside the parentheses is all under the square root sign.  

So, the square root of y + the square root of y+7 = 7

 

 

 

I know that y can equal 9 but not sure how to get there.

 

Thanks.  

 

 

Answer 1

√y + √(y+7) = 7

 

Rearranging terms:

 

√y - 7 = -√(y+7)

 

Square both sides:

 

y - 14√y + 49 = y + 7

 

Combine like terms:

 

42 = 14√y

 

42/14 = √y

 

3 = √y

 

Square both sides:

 

9 = y