Solve (2*sqrt{5}i-3sqrt{14})divsqrt{6}

$$( 2 \times \sqrt { 5 } i - 3 \sqrt { 14 } ) \div \sqrt { 6 }$$

Evaluate

$$\frac{\sqrt{30}i}{3}-\frac{2\sqrt{21}}{2}\approx -4.582575695+1.825741858i$$

Solution Steps

Rationalize the denominator of \frac{2i\sqrt{5}-3\sqrt{14}}{\sqrt{6}} by multiplying numerator and denominator by \sqrt{6}.

$$\frac{\left(2i\sqrt{5}-3\sqrt{14}\right)\sqrt{6}}{\left(\sqrt{6}\right)^{2}}$$

The square of \sqrt{6} is 6.

$$\frac{\left(2i\sqrt{5}-3\sqrt{14}\right)\sqrt{6}}{6}$$

Use the distributive property to multiply 2i\sqrt{5}-3\sqrt{14} by \sqrt{6}.

$$\frac{2i\sqrt{5}\sqrt{6}-3\sqrt{14}\sqrt{6}}{6}$$

To multiply \sqrt{5} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{2i\sqrt{30}-3\sqrt{14}\sqrt{6}}{6}$$

To multiply \sqrt{14} and \sqrt{6}, multiply the numbers under the square root.

$$\frac{2i\sqrt{30}-3\sqrt{84}}{6}$$

Factor 84=2^{2}\times 21. Rewrite the square root of the product \sqrt{2^{2}\times 21} as the product of square roots \sqrt{2^{2}}\sqrt{21}. Take the square root of 2^{2}.

$$\frac{2i\sqrt{30}-3\times 2\sqrt{21}}{6}$$

Multiply -3 and 2 to get -6.

$$\frac{2i\sqrt{30}-6\sqrt{21}}{6}$$

Real Part

$$-\sqrt{21}$$