Solve sqrt{2*2*3*3*3}

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

Evaluate

$$6\sqrt{3}\approx 10.392304845$$

Solution Steps

Multiply 2 and 2 to get 4.

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

Multiply 4 and 3 to get 12.

$$\sqrt{12\times 3\times 3}$$

Multiply 12 and 3 to get 36.

$$\sqrt{36\times 3}$$

Multiply 36 and 3 to get 108.

$$\sqrt{108}$$

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$6\sqrt{3}$$