Solve asqrt{b}-sqrt{a}=5

$$a \sqrt { b } - \sqrt { a } = 5$$

Solve for b

$$b=\left(\frac{\sqrt{a}+5}{a}\right)^{2}$$

$$a>0$$

Steps for Solving Radical Equations

Subtract -\sqrt{a} from both sides of the equation.

$$a\sqrt{b}-\sqrt{a}-\left(-\sqrt{a}\right)=5-\left(-\sqrt{a}\right)$$

Subtracting -\sqrt{a} from itself leaves 0.

$$a\sqrt{b}=5-\left(-\sqrt{a}\right)$$

Subtract -\sqrt{a} from 5.

$$a\sqrt{b}=\sqrt{a}+5$$

Divide both sides by a.

$$\frac{a\sqrt{b}}{a}=\frac{\sqrt{a}+5}{a}$$

Dividing by a undoes the multiplication by a.

$$\sqrt{b}=\frac{\sqrt{a}+5}{a}$$

Square both sides of the equation.

$$b=\frac{\left(\sqrt{a}+5\right)^{2}}{a^{2}}$$

Solve for a

$$a=\frac{\left(\sqrt{20\sqrt{b}+1}+1\right)^{2}}{4b}$$

$$b>0$$