Solve 3sqrt{72}+5sqrt{18}

$$3 \sqrt{ 72 } +5 \sqrt{ 18 }$$

Evaluate

$$33\sqrt{2}\approx 46.669047558$$

Solution Steps

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}.

$$3\times 6\sqrt{2}+5\sqrt{18}$$

Multiply 3 and 6 to get 18.

$$18\sqrt{2}+5\sqrt{18}$$

Factor 18=3^{2}\times 2. Rewrite the square root of the product \sqrt{3^{2}\times 2} as the product of square roots \sqrt{3^{2}}\sqrt{2}. Take the square root of 3^{2}.

$$18\sqrt{2}+5\times 3\sqrt{2}$$

Multiply 5 and 3 to get 15.

$$18\sqrt{2}+15\sqrt{2}$$

Combine 18\sqrt{2} and 15\sqrt{2} to get 33\sqrt{2}.

$$33\sqrt{2}$$