Solve 2sqrt{50}*3sqrt{32}*4

$$2 \sqrt { 50 } \times 3 \sqrt { 32 } \times 4$$

Evaluate

$$960$$

Solution Steps

Multiply 2 and 3 to get 6.

$$6\times 4\sqrt{50}\sqrt{32}$$

Multiply 6 and 4 to get 24.

$$24\sqrt{50}\sqrt{32}$$

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}.

$$24\times 5\sqrt{2}\sqrt{32}$$

Multiply 24 and 5 to get 120.

$$120\sqrt{2}\sqrt{32}$$

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}.

$$120\sqrt{2}\times 4\sqrt{2}$$

Multiply 120 and 4 to get 480.

$$480\sqrt{2}\sqrt{2}$$

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

$$480\times 2$$

Multiply 480 and 2 to get 960.

$$960$$

Factor

$$2^{6}\times 3\times 5$$