# How do you solve sqrt(y+21)-1=sqrt(y+12)?

Oct 17, 2015

The solution is $y = 4$.

#### Explanation:

Square both terms:

$y + 21 - 2 \sqrt{y + 21} + 1 = y + 12$.

Isolate the root:

$y + 21 - y - 12 + 1 = 2 \sqrt{y + 21}$, which simplifies into

$2 \sqrt{y + 21} = 10$

Square both terms again:

$4 \left(y + 21\right) = 100 \setminus \iff 4 y + 84 = 100 \setminus \iff 4 y = 16$.

Solving by $y$, we get $y = 4$.

This solution is acceptable, since both the original square roots are well defined in that point.