Solve 3sqrt{xsqrt{2}}=2sqrt{x}

$$3 \sqrt{ x \sqrt{ 2 } } =2 \sqrt{ x }$$

Solve for x

$$x=0$$

Solution Steps

Square both sides of the equation.

$$\left(3\sqrt{x\sqrt{2}}\right)^{2}=\left(2\sqrt{x}\right)^{2}$$

Expand \left(3\sqrt{x\sqrt{2}}\right)^{2}.

$$3^{2}\left(\sqrt{x\sqrt{2}}\right)^{2}=\left(2\sqrt{x}\right)^{2}$$

Calculate 3 to the power of 2 and get 9.

$$9\left(\sqrt{x\sqrt{2}}\right)^{2}=\left(2\sqrt{x}\right)^{2}$$

Calculate \sqrt{x\sqrt{2}} to the power of 2 and get x\sqrt{2}.

$$9x\sqrt{2}=\left(2\sqrt{x}\right)^{2}$$

Expand \left(2\sqrt{x}\right)^{2}.

$$9x\sqrt{2}=2^{2}\left(\sqrt{x}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$9x\sqrt{2}=4\left(\sqrt{x}\right)^{2}$$

Calculate \sqrt{x} to the power of 2 and get x.

$$9x\sqrt{2}=4x$$

Subtract 4x from both sides.

$$9x\sqrt{2}-4x=0$$

Combine all terms containing x.

$$\left(9\sqrt{2}-4\right)x=0$$

Divide 0 by 9\sqrt{2}-4.

$$x=0$$

Substitute 0 for x in the equation 3\sqrt{x\sqrt{2}}=2\sqrt{x}.

$$3\sqrt{0\sqrt{2}}=2\sqrt{0}$$

Simplify. The value x=0 satisfies the equation.

$$0=0$$

Equation 3\sqrt{\sqrt{2}x}=2\sqrt{x} has a unique solution.

$$x=0$$