Solve i+14/sqrt{7}-sqrt{28}

$$i + \frac { 14 } { \sqrt { 7 } } - \sqrt { 28 }$$

Evaluate

$$i$$

Solution Steps

Rationalize the denominator of \frac{14}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$i+\frac{14\sqrt{7}}{\left(\sqrt{7}\right)^{2}}-\sqrt{28}$$

The square of \sqrt{7} is 7.

$$i+\frac{14\sqrt{7}}{7}-\sqrt{28}$$

Divide 14\sqrt{7} by 7 to get 2\sqrt{7}.

$$i+2\sqrt{7}-\sqrt{28}$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$i+2\sqrt{7}-2\sqrt{7}$$

Combine 2\sqrt{7} and -2\sqrt{7} to get 0.

$$i$$

Real Part

$$0$$

Solution Steps

Rationalize the denominator of \frac{14}{\sqrt{7}} by multiplying numerator and denominator by \sqrt{7}.

$$Re(i+\frac{14\sqrt{7}}{\left(\sqrt{7}\right)^{2}}-\sqrt{28})$$

The square of \sqrt{7} is 7.

$$Re(i+\frac{14\sqrt{7}}{7}-\sqrt{28})$$

Divide 14\sqrt{7} by 7 to get 2\sqrt{7}.

$$Re(i+2\sqrt{7}-\sqrt{28})$$

Factor 28=2^{2}\times 7. Rewrite the square root of the product \sqrt{2^{2}\times 7} as the product of square roots \sqrt{2^{2}}\sqrt{7}. Take the square root of 2^{2}.

$$Re(i+2\sqrt{7}-2\sqrt{7})$$

Combine 2\sqrt{7} and -2\sqrt{7} to get 0.

$$Re(i)$$

The real part of i is 0.

$$0$$