Solve sqrt{243}+sqrt{243}+8*sqrt{2}+8*sqrt{2}

$$\sqrt{ 243 } + \sqrt{ 243 } +8 \times \sqrt{ 2 } +8 \times \sqrt{ 2 }$$

Evaluate

$$16\sqrt{2}+18\sqrt{3}\approx 53.804331534$$

Solution Steps

Factor 243=9^{2}\times 3. Rewrite the square root of the product \sqrt{9^{2}\times 3} as the product of square roots \sqrt{9^{2}}\sqrt{3}. Take the square root of 9^{2}.

$$9\sqrt{3}+\sqrt{243}+8\sqrt{2}+8\sqrt{2}$$

Factor 243=9^{2}\times 3. Rewrite the square root of the product \sqrt{9^{2}\times 3} as the product of square roots \sqrt{9^{2}}\sqrt{3}. Take the square root of 9^{2}.

$$9\sqrt{3}+9\sqrt{3}+8\sqrt{2}+8\sqrt{2}$$

Combine 9\sqrt{3} and 9\sqrt{3} to get 18\sqrt{3}.

$$18\sqrt{3}+8\sqrt{2}+8\sqrt{2}$$

Combine 8\sqrt{2} and 8\sqrt{2} to get 16\sqrt{2}.

$$18\sqrt{3}+16\sqrt{2}$$