Solve 3sqrt{6}*5sqrt{32}

$$3 \sqrt { 6 } \times 5 \sqrt { 32 }$$

Evaluate

$$120\sqrt{3}\approx 207.846096908$$

Solution Steps

Multiply 3 and 5 to get 15.

$$15\sqrt{6}\sqrt{32}$$

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}.

$$15\sqrt{6}\times 4\sqrt{2}$$

Multiply 15 and 4 to get 60.

$$60\sqrt{6}\sqrt{2}$$

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}.

$$60\sqrt{2}\sqrt{3}\sqrt{2}$$

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

$$60\times 2\sqrt{3}$$

Multiply 60 and 2 to get 120.

$$120\sqrt{3}$$