Solve 4sqrt[2]{8*4}-3*4/5sqrt{50*4^3}

$$4 \sqrt[ 2 ] { 8 \times 4 } - \frac { 3 \times 4 } { 5 } \sqrt { 50 \times 4 ^ { 3 } }$$

Evaluate

$$-80\sqrt{2}\approx -113.13708499$$

Solution Steps

Multiply 8 and 4 to get 32.

$$4\sqrt[2]{32}-\frac{3\times 4}{5}\sqrt{50\times 4^{3}}$$

Multiply 3 and 4 to get 12.

$$4\sqrt[2]{32}-\frac{12}{5}\sqrt{50\times 4^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$4\sqrt[2]{32}-\frac{12}{5}\sqrt{50\times 64}$$

Multiply 50 and 64 to get 3200.

$$4\sqrt[2]{32}-\frac{12}{5}\sqrt{3200}$$

Factor 3200=40^{2}\times 2. Rewrite the square root of the product \sqrt{40^{2}\times 2} as the product of square roots \sqrt{40^{2}}\sqrt{2}. Take the square root of 40^{2}.

$$4\sqrt[2]{32}-\frac{12}{5}\times 40\sqrt{2}$$

Multiply \frac{12}{5} and 40 to get 96.

$$4\sqrt[2]{32}-96\sqrt{2}$$