Solve frac{sqrt{50}*sqrt{32}}{sqrt{8}}-4sqrt{2}

$$\frac { \sqrt { 50 } \times \sqrt { 32 } } { \sqrt { 8 } } - 4 \sqrt { 2 }$$

Evaluate

$$6\sqrt{2}\approx 8.485281374$$

Solution Steps

Factor 50=5^{2}\times 2. Rewrite the square root of the product \sqrt{5^{2}\times 2} as the product of square roots \sqrt{5^{2}}\sqrt{2}. Take the square root of 5^{2}.

$$\frac{5\sqrt{2}\sqrt{32}}{\sqrt{8}}-4\sqrt{2}$$

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}.

$$\frac{5\sqrt{2}\times 4\sqrt{2}}{\sqrt{8}}-4\sqrt{2}$$

Multiply 5 and 4 to get 20.

$$\frac{20\sqrt{2}\sqrt{2}}{\sqrt{8}}-4\sqrt{2}$$

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

$$\frac{20\times 2}{\sqrt{8}}-4\sqrt{2}$$

Multiply 20 and 2 to get 40.

$$\frac{40}{\sqrt{8}}-4\sqrt{2}$$

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}.

$$\frac{40}{2\sqrt{2}}-4\sqrt{2}$$

Rationalize the denominator of \frac{40}{2\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$\frac{40\sqrt{2}}{2\left(\sqrt{2}\right)^{2}}-4\sqrt{2}$$

The square of \sqrt{2} is 2.

$$\frac{40\sqrt{2}}{2\times 2}-4\sqrt{2}$$

Cancel out 2\times 2 in both numerator and denominator.

$$10\sqrt{2}-4\sqrt{2}$$

Combine 10\sqrt{2} and -4\sqrt{2} to get 6\sqrt{2}.

$$6\sqrt{2}$$