Solve 2sqrt{216}+4sqrt{72}=

$$2 \sqrt { 216 } + 4 \sqrt { 72 } =$$

Evaluate

$$12\left(\sqrt{6}+2\sqrt{2}\right)\approx 63.33500241$$

Solution Steps

Factor 216=6^{2}\times 6. Rewrite the square root of the product \sqrt{6^{2}\times 6} as the product of square roots \sqrt{6^{2}}\sqrt{6}. Take the square root of 6^{2}.

$$2\times 6\sqrt{6}+4\sqrt{72}$$

Multiply 2 and 6 to get 12.

$$12\sqrt{6}+4\sqrt{72}$$

Factor 72=6^{2}\times 2. Rewrite the square root of the product \sqrt{6^{2}\times 2} as the product of square roots \sqrt{6^{2}}\sqrt{2}. Take the square root of 6^{2}.

$$12\sqrt{6}+4\times 6\sqrt{2}$$

Multiply 4 and 6 to get 24.

$$12\sqrt{6}+24\sqrt{2}$$

Factor

$$12 {(\sqrt{6} + 2 \sqrt{2})} = 63.33500241$$