Solve sqrt{3*18}*sqrt{3*54}

$$\sqrt{ 3 \times 18 } \times \sqrt{ 3 \times 54 }$$

Evaluate

$$54\sqrt{3}\approx 93.530743609$$

Solution Steps

Multiply 3 and 18 to get 54.

$$\sqrt{54}\sqrt{3\times 54}$$

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$3\sqrt{6}\sqrt{3\times 54}$$

Multiply 3 and 54 to get 162.

$$3\sqrt{6}\sqrt{162}$$

Factor 162=9^{2}\times 2. Rewrite the square root of the product \sqrt{9^{2}\times 2} as the product of square roots \sqrt{9^{2}}\sqrt{2}. Take the square root of 9^{2}.

$$3\sqrt{6}\times 9\sqrt{2}$$

Multiply 3 and 9 to get 27.

$$27\sqrt{6}\sqrt{2}$$

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}.

$$27\sqrt{2}\sqrt{3}\sqrt{2}$$

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

$$27\times 2\sqrt{3}$$

Multiply 27 and 2 to get 54.

$$54\sqrt{3}$$