Solve (2sqrt{3}-sqrt{6})+6*4/sqrt{2}

$$(2 \sqrt{ 3 } - \sqrt{ 6 } )+6 \times \frac{ 4 }{ \sqrt{ 2 } }$$

Evaluate

$$2\sqrt{3}+12\sqrt{2}-\sqrt{6}\approx 17.985174621$$

Solution Steps

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

$$2\sqrt{3}-\sqrt{6}+6\times \frac{4\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$2\sqrt{3}-\sqrt{6}+6\times \frac{4\sqrt{2}}{2}$$

Divide 4\sqrt{2} by 2 to get 2\sqrt{2}.

$$2\sqrt{3}-\sqrt{6}+6\times 2\sqrt{2}$$

Multiply 6 and 2 to get 12.

$$2\sqrt{3}-\sqrt{6}+12\sqrt{2}$$