Solve 2sqrt{72}*5sqrt{32}*3sqrt{50}

$$2 \sqrt { 72 } \times 5 \sqrt { 32 } \times 3 \sqrt { 50 }$$

Evaluate

$$7200\sqrt{2}\approx 10182.337649086$$

Solution Steps

Multiply 2 and 3 to get 6.

$$6\times 5\sqrt{72}\sqrt{32}\sqrt{50}$$

Multiply 6 and 5 to get 30.

$$30\sqrt{72}\sqrt{32}\sqrt{50}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$30\times 6\sqrt{2}\sqrt{32}\sqrt{50}$$

Multiply 30 and 6 to get 180.

$$180\sqrt{2}\sqrt{32}\sqrt{50}$$

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}.

$$180\sqrt{2}\times 4\sqrt{2}\sqrt{50}$$

Multiply 180 and 4 to get 720.

$$720\sqrt{2}\sqrt{2}\sqrt{50}$$

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

$$720\times 2\sqrt{50}$$

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}.

$$720\times 2\times 5\sqrt{2}$$

Multiply 720 and 5 to get 3600.

$$3600\times 2\sqrt{2}$$

Multiply 3600 and 2 to get 7200.

$$7200\sqrt{2}$$