Solve sqrt{48}+5sqrt{75}+2sqrt{81}-sqrt{108}

$$\sqrt { 48 } + 5 \sqrt { 75 } + 2 \sqrt { 81 } - \sqrt { 108 }$$

Evaluate

$$23\sqrt{3}+18\approx 57.837168574$$

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}.

$$4\sqrt{3}+5\sqrt{75}+2\sqrt{81}-\sqrt{108}$$

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}.

$$4\sqrt{3}+5\times 5\sqrt{3}+2\sqrt{81}-\sqrt{108}$$

Multiply 5 and 5 to get 25.

$$4\sqrt{3}+25\sqrt{3}+2\sqrt{81}-\sqrt{108}$$

Combine 4\sqrt{3} and 25\sqrt{3} to get 29\sqrt{3}.

$$29\sqrt{3}+2\sqrt{81}-\sqrt{108}$$

Calculate the square root of 81 and get 9.

$$29\sqrt{3}+2\times 9-\sqrt{108}$$

Multiply 2 and 9 to get 18.

$$29\sqrt{3}+18-\sqrt{108}$$

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}.

$$29\sqrt{3}+18-6\sqrt{3}$$

Combine 29\sqrt{3} and -6\sqrt{3} to get 23\sqrt{3}.

$$23\sqrt{3}+18$$