Solve sqrt{30}*8sqrt{40}

$$\sqrt { 30 } \cdot 8 \sqrt { 40 }$$

Evaluate

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

Solution Steps

Factor 40=2^{2}\times 10. Rewrite the square root of the product \sqrt{2^{2}\times 10} as the product of square roots \sqrt{2^{2}}\sqrt{10}. Take the square root of 2^{2}.

$$8\sqrt{30}\times 2\sqrt{10}$$

Multiply 8 and 2 to get 16.

$$16\sqrt{30}\sqrt{10}$$

Factor 30=10\times 3. Rewrite the square root of the product \sqrt{10\times 3} as the product of square roots \sqrt{10}\sqrt{3}.

$$16\sqrt{10}\sqrt{3}\sqrt{10}$$

Multiply \sqrt{10} and \sqrt{10} to get 10.

$$16\times 10\sqrt{3}$$

Multiply 16 and 10 to get 160.

$$160\sqrt{3}$$