Solve sqrt{50}*4sqrt{96}

$$\sqrt { 50 } \times 4 \sqrt { 96 }$$

Evaluate

$$160\sqrt{3}\approx 277.128129211$$

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}.

$$4\times 5\sqrt{2}\sqrt{96}$$

Multiply 4 and 5 to get 20.

$$20\sqrt{2}\sqrt{96}$$

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

$$20\sqrt{2}\times 4\sqrt{6}$$

Multiply 20 and 4 to get 80.

$$80\sqrt{2}\sqrt{6}$$

Factor 6=2\times 3. Rewrite the square root of the product \sqrt{2\times 3} as the product of square roots \sqrt{2}\sqrt{3}.

$$80\sqrt{2}\sqrt{2}\sqrt{3}$$

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

$$80\times 2\sqrt{3}$$

Multiply 80 and 2 to get 160.

$$160\sqrt{3}$$