Solve 6divsqrt{2}*2/sqrt{2}

$$6 \div \sqrt { 2 } \times \frac { 2 } { \sqrt { 2 } }$$

Evaluate

$$6$$

Solution Steps

Rationalize the denominator of \frac{6}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{6\sqrt{2}}{\left(\sqrt{2}\right)^{2}}\times \frac{2}{\sqrt{2}}$$

The square of \sqrt{2} is 2.

$$\frac{6\sqrt{2}}{2}\times \frac{2}{\sqrt{2}}$$

Divide 6\sqrt{2} by 2 to get 3\sqrt{2}.

$$3\sqrt{2}\times \frac{2}{\sqrt{2}}$$

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

$$3\sqrt{2}\times \frac{2\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$3\sqrt{2}\times \frac{2\sqrt{2}}{2}$$

Cancel out 2 and 2.

$$3\sqrt{2}\sqrt{2}$$

Multiply \sqrt{2} and \sqrt{2} to get 2.

$$3\times 2$$

Multiply 3 and 2 to get 6.

$$6$$

Factor

$$2\times 3$$