Solve sqrt{1}sqrt{2}sqrt{3}sqrt{4}

$$\sqrt{ 1 } \sqrt{ 2 } \sqrt{ 3 } \sqrt{ 4 }$$

Evaluate

$$2\sqrt{6}\approx 4.898979486$$

Solution Steps

Factor 2=1\times 2. Rewrite the square root of the product \sqrt{1\times 2} as the product of square roots \sqrt{1}\sqrt{2}.

$$\sqrt{1}\sqrt{1}\sqrt{2}\sqrt{3}\sqrt{4}$$

Multiply \sqrt{1} and \sqrt{1} to get 1.

$$1\sqrt{2}\sqrt{3}\sqrt{4}$$

Factor 4=2\times 2. Rewrite the square root of the product \sqrt{2\times 2} as the product of square roots \sqrt{2}\sqrt{2}.

$$1\sqrt{2}\sqrt{3}\sqrt{2}\sqrt{2}$$

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

$$1\times 2\sqrt{3}\sqrt{2}$$

Multiply 1 and 2 to get 2.

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

To multiply \sqrt{3} and \sqrt{2}, multiply the numbers under the square root.

$$2\sqrt{6}$$