Solve sqrt{32}*2sqrt{1/2}divsqrt{2}

$$\sqrt { 32 } \times 2 \sqrt { \frac { 1 } { 2 } } \div \sqrt { 2 }$$

Evaluate

$$4\sqrt{2}\approx 5.656854249$$

Solution Steps

Factor 32=4^{2}\times 2. Rewrite the square root of the product \sqrt{4^{2}\times 2} as the product of square roots \sqrt{4^{2}}\sqrt{2}. Take the square root of 4^{2}.

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

Multiply 2 and 4 to get 8.

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

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

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

Calculate the square root of 1 and get 1.

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

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

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

The square of \sqrt{2} is 2.

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

Cancel out 2, the greatest common factor in 8 and 2.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Multiply 4 and 2 to get 8.

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

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

$$4\sqrt{2}$$