Solve 2sqrt{8}divsqrt{1/2}*sqrt{2}

$$2 \sqrt { 8 } \div \sqrt { \frac { 1 } { 2 } } \times \sqrt { 2 }$$

Evaluate

$$8\sqrt{2}\approx 11.313708499$$

Solution Steps

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$\frac{2\times 2\sqrt{2}}{\sqrt{\frac{1}{2}}}\sqrt{2}$$

Multiply 2 and 2 to get 4.

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

Rewrite the square root of the division \sqrt{\frac{1}{2}} as the division of square roots \frac{\sqrt{1}}{\sqrt{2}}.

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

Calculate the square root of 1 and get 1.

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

Rationalize the denominator of \frac{1}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

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

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

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

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

The square of \sqrt{2} is 2.

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

Multiply 4 and 2 to get 8.

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

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

$$\frac{8\times 2}{2}\sqrt{2}$$

Multiply 8 and 2 to get 16.

$$\frac{16}{2}\sqrt{2}$$

Divide 16 by 2 to get 8.

$$8\sqrt{2}$$