Solve sqrt{2}*sqrt{5}quadtext{(2)}sqrt{3}*sqrt{12}

$$\sqrt { 2 } \times \sqrt { 5 } \quad \text { (2) } \sqrt { 3 } \times \sqrt { 12 }$$

Evaluate

$$12\sqrt{10}\approx 37.947331922$$

Solution Steps

Factor 12=2\times 6. Rewrite the square root of the product \sqrt{2\times 6} as the product of square roots \sqrt{2}\sqrt{6}.

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

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

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

Factor 6=3\times 2. Rewrite the square root of the product \sqrt{3\times 2} as the product of square roots \sqrt{3}\sqrt{2}.

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

Multiply \sqrt{3} and \sqrt{3} to get 3.

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

Multiply 2 and 2 to get 4.

$$4\sqrt{5}\times 3\sqrt{2}$$

Multiply 4 and 3 to get 12.

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

To multiply \sqrt{5} and \sqrt{2}, multiply the numbers under the square root.

$$12\sqrt{10}$$