Solve sqrt{12sqrt{48}sqrt{27}}

$$\sqrt{ 12 \sqrt{ 48 } \sqrt{ 27 } }$$

Evaluate

$$12\sqrt{3}\approx 20.784609691$$

Solution Steps

Factor 48=4^{2}\times 3. Rewrite the square root of the product \sqrt{4^{2}\times 3} as the product of square roots \sqrt{4^{2}}\sqrt{3}. Take the square root of 4^{2}.

$$\sqrt{12\times 4\sqrt{3}\sqrt{27}}$$

Multiply 12 and 4 to get 48.

$$\sqrt{48\sqrt{3}\sqrt{27}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$\sqrt{48\sqrt{3}\times 3\sqrt{3}}$$

Multiply 48 and 3 to get 144.

$$\sqrt{144\sqrt{3}\sqrt{3}}$$

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

$$\sqrt{144\times 3}$$

Multiply 144 and 3 to get 432.

$$\sqrt{432}$$

Factor 432=12^{2}\times 3. Rewrite the square root of the product \sqrt{12^{2}\times 3} as the product of square roots \sqrt{12^{2}}\sqrt{3}. Take the square root of 12^{2}.

$$12\sqrt{3}$$