Solve 3sqrt{32}*sqrt{50}

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

Evaluate

$$120$$

Solution Steps

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}.

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

Multiply 3 and 4 to get 12.

$$12\sqrt{2}\sqrt{50}$$

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}.

$$12\sqrt{2}\times 5\sqrt{2}$$

Multiply 12 and 5 to get 60.

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

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

$$60\times 2$$

Multiply 60 and 2 to get 120.

$$120$$

Factor

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