Solve 2^2+x^2/sqrt{2}

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

Evaluate

$$\frac{\sqrt{2}\left(x^{2}+4\right)}{2}$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\frac{4+x^{2}}{\sqrt{2}}$$

Rationalize the denominator of \frac{4+x^{2}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{\left(4+x^{2}\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$\frac{\left(4+x^{2}\right)\sqrt{2}}{2}$$

Use the distributive property to multiply 4+x^{2} by \sqrt{2}.

$$\frac{4\sqrt{2}+x^{2}\sqrt{2}}{2}$$

Factor

$$\frac{\sqrt{2}\left(x^{2}+4\right)}{2}$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$factor(\frac{4+x^{2}}{\sqrt{2}})$$

Rationalize the denominator of \frac{4+x^{2}}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$factor(\frac{\left(4+x^{2}\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}})$$

The square of \sqrt{2} is 2.

$$factor(\frac{\left(4+x^{2}\right)\sqrt{2}}{2})$$

Use the distributive property to multiply 4+x^{2} by \sqrt{2}.

$$factor(\frac{4\sqrt{2}+x^{2}\sqrt{2}}{2})$$

Consider 4\sqrt{2}+x^{2}\sqrt{2}. Factor out \sqrt{2}.

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

Rewrite the complete factored expression. Polynomial 4+x^{2} is not factored since it does not have any rational roots.

$$\frac{\left(4+x^{2}\right)\sqrt{2}}{2}$$