Solve 72sqrt{108}+2sqrt{27}+2sqrt{75}

$$72 \sqrt { 108 } + 2 \sqrt { 27 } + 2 \sqrt { 75 }$$

Evaluate

$$448\sqrt{3}\approx 775.958761791$$

Solution Steps

Factor 108=6^{2}\times 3. Rewrite the square root of the product \sqrt{6^{2}\times 3} as the product of square roots \sqrt{6^{2}}\sqrt{3}. Take the square root of 6^{2}.

$$72\times 6\sqrt{3}+2\sqrt{27}+2\sqrt{75}$$

Multiply 72 and 6 to get 432.

$$432\sqrt{3}+2\sqrt{27}+2\sqrt{75}$$

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}.

$$432\sqrt{3}+2\times 3\sqrt{3}+2\sqrt{75}$$

Multiply 2 and 3 to get 6.

$$432\sqrt{3}+6\sqrt{3}+2\sqrt{75}$$

Combine 432\sqrt{3} and 6\sqrt{3} to get 438\sqrt{3}.

$$438\sqrt{3}+2\sqrt{75}$$

Factor 75=5^{2}\times 3. Rewrite the square root of the product \sqrt{5^{2}\times 3} as the product of square roots \sqrt{5^{2}}\sqrt{3}. Take the square root of 5^{2}.

$$438\sqrt{3}+2\times 5\sqrt{3}$$

Multiply 2 and 5 to get 10.

$$438\sqrt{3}+10\sqrt{3}$$

Combine 438\sqrt{3} and 10\sqrt{3} to get 448\sqrt{3}.

$$448\sqrt{3}$$