Solve frac{2sqrt{2}}{1/2}=4/sqrt{2/2}

$$\frac{ 2 \sqrt{ 2 } }{ \frac{ 1 }{ 2 } } = \frac{ 4 }{ \frac{ \sqrt{ 2 } }{ 2 } }$$

Verify

Solution Steps

Divide 2\sqrt{2} by \frac{1}{2} by multiplying 2\sqrt{2} by the reciprocal of \frac{1}{2}.

$$2\sqrt{2}\times 2=\frac{4}{\frac{\sqrt{2}}{2}}$$

Multiply 2 and 2 to get 4.

$$4\sqrt{2}=\frac{4}{\frac{\sqrt{2}}{2}}$$

Divide 4 by \frac{\sqrt{2}}{2} by multiplying 4 by the reciprocal of \frac{\sqrt{2}}{2}.

$$4\sqrt{2}=\frac{4\times 2}{\sqrt{2}}$$

Multiply 4 and 2 to get 8.

$$4\sqrt{2}=\frac{8}{\sqrt{2}}$$

Rationalize the denominator of \frac{8}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$4\sqrt{2}=\frac{8\sqrt{2}}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$4\sqrt{2}=\frac{8\sqrt{2}}{2}$$

Divide 8\sqrt{2} by 2 to get 4\sqrt{2}.

$$4\sqrt{2}=4\sqrt{2}$$

Subtract 4\sqrt{2} from both sides.

$$4\sqrt{2}-4\sqrt{2}=0$$

Combine 4\sqrt{2} and -4\sqrt{2} to get 0.

$$0=0$$

Compare 0 and 0.

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