Evaluate the Limit, MultiVariable functions

Lim (x^2 + y^2) / ( sqrt(x^2 + y^2 +1) - 1 )
(x,y)-> (0,0)

I can't figure it out how to prove that this exist. I think its based off maybe squeeze theorem but I don't know how to quite apply it in this situation.

Note that the only expression in x and y that repeatedly appears is x^2 + y^2.
So let z = x^2 + y^2. Note that as (x,y)-> (0,0), z -> 0 as well.
Therefore,

Lim (x^2 + y^2) / ( sqrt(x^2 + y^2 +1) - 1 )
(x,y)-> (0,0)

= Lim z / ( sqrt(z +1) - 1 )
z -> 0

= Lim z( sqrt(z +1) + 1 ) / [( sqrt(z +1) - 1 )( sqrt(z +1) + 1 )]
z -> 0

= Lim z( sqrt(z +1) + 1 ) / (z + 1 - 1)
z -> 0

= Lim z( sqrt(z +1) + 1 ) / z
z -> 0

= Lim ( sqrt(z +1) + 1 )
z -> 0

= sqrt(0 +1) + 1
= 2.

The limit is 2.

Lord bless you today!

lim{(x,y)→(0,0)} (x² + y²) / [√(x² + y² + 1) - 1]

Multiply and divide by the conjugate:
lim{(x,y)→(0,0)} (x² + y²)[√(x² + y² + 1) + 1] / [√(x² + y² + 1) - 1][√(x² + y² + 1) + 1]

Simplify the denominator:
lim{(x,y)→(0,0)} (x² + y²)[√(x² + y² + 1) + 1] / (x² + y²)

Cancel common terms:
lim{(x,y)→(0,0)} [√(x² + y² + 1) + 1]

Apply the limit:
[√(0² + 0² + 1) + 1] = 2