Solve sqrt{a}=bsqrt{hk}

$$\sqrt { a } = b \sqrt { h k }$$

Solve for a

$$a=hkb^{2}$$

$$\left(b\geq 0\text{ and }h\leq 0\text{ and }k\leq 0\right)\text{ or }\left(b\geq 0\text{ and }k\geq 0\text{ and }h\geq 0\right)\text{ or }h=0\text{ or }k=0$$

Steps for Solving Radical Equations

Square both sides of the equation.

$$a=hkb^{2}$$

Solve for a (complex solution)

$$a=hkb^{2}$$

$$arg(b\sqrt{hk})<\pi \text{ or }k=0\text{ or }h=0\text{ or }b=0$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=\left(hk\right)^{-\frac{1}{2}}\sqrt{a}\text{, }&k\neq 0\text{ and }h\neq 0\\b\in \mathrm{C}\text{, }&\left(h=0\text{ or }k=0\right)\text{ and }a=0\end{matrix}\right.$$

Solve for b

$$\left\{\begin{matrix}b=\sqrt{\frac{a}{hk}}\text{, }&\left(h<0\text{ and }k<0\text{ and }a\geq 0\right)\text{ or }\left(k>0\text{ and }h>0\text{ and }a\geq 0\right)\\b\in \mathrm{R}\text{, }&\left(h=0\text{ or }k=0\right)\text{ and }a=0\end{matrix}\right.$$