Solve xsqrt{2-4}+x^2sqrt{3-4}

$$x \sqrt{ 2-4 } + { x }^{ 2 } \sqrt{ 3-4 }$$

Evaluate (complex solution)

$$ix\left(x+\sqrt{2}\right)$$

Solution Steps

Subtract 4 from 2 to get -2.

$$x\sqrt{-2}+x^{2}\sqrt{3-4}$$

Factor -2=2\left(-1\right). Rewrite the square root of the product \sqrt{2\left(-1\right)} as the product of square roots \sqrt{2}\sqrt{-1}. By definition, the square root of -1 is i.

$$x\sqrt{2}i+x^{2}\sqrt{3-4}$$

Subtract 4 from 3 to get -1.

$$x\sqrt{2}i+x^{2}\sqrt{-1}$$

Calculate the square root of -1 and get i.

$$x\sqrt{2}i+x^{2}i$$

Evaluate

$$\text{Indeterminate}$$

Solution Steps

Subtract 4 from 2 to get -2.

$$x\sqrt{-2}+x^{2}\sqrt{3-4}$$

Subtract 4 from 3 to get -1.

$$x\sqrt{-2}+x^{2}\sqrt{-1}$$

Factor (complex solution)

$$x\left(ix+\sqrt{2}i\right)$$

Solution Steps

Factor out x.

$$x\left(i\sqrt{2}+ix\right)$$