# If sqrt(u) + sqrt(v) - sqrt(w) = 0, then find the value of (u+v-w)?

## If $\sqrt{u} + \sqrt{v} - \sqrt{w} = 0$, then find the value of $\left(u + v - w\right)$.

Jul 17, 2018

See a solution process below:

#### Explanation:

First, solve for $w$

$\sqrt{u} + \sqrt{v} - \sqrt{w} = 0$

$\sqrt{u} + \sqrt{v} - \sqrt{w} + \sqrt{w} = 0 + \sqrt{w}$

$\sqrt{u} + \sqrt{v} - 0 = \sqrt{w}$

$\sqrt{u} + \sqrt{v} = \sqrt{w}$

${\left(\sqrt{u} + \sqrt{v}\right)}^{2} = {\left(\sqrt{w}\right)}^{2}$

${\left(\sqrt{u}\right)}^{2} + 2 \sqrt{u} \sqrt{v} + {\left(\sqrt{v}\right)}^{2} = w$

$u + 2 \sqrt{u} \sqrt{v} + v = w$

Substituting the left side of the equation for the $w$ in the expression gives:

$\left(u + v - w\right)$ becomes:

$\left(u + v - \left(u + 2 \sqrt{u} \sqrt{v} + v\right)\right) \implies$

$\left(u + v - u - 2 \sqrt{u} \sqrt{v} - v\right) \implies$

$\left(u - u + v - v - 2 \sqrt{u} \sqrt{v}\right) \implies$

$\left(0 + 0 - 2 \sqrt{u} \sqrt{v}\right) \implies$

$- 2 \sqrt{u} \sqrt{v}$