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

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

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}.

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

Multiply 2 and 2 to get 4.

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

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

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

The square of \sqrt{2} is 2.

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

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

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

Multiply 4 and 2 to get 8.

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

Divide 8 by 2 to get 4.

$$4\sqrt{8}$$

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}.

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

Multiply 4 and 2 to get 8.

$$8\sqrt{2}$$