Solve 2sqrt{75}-sqrt{12}-sqrt{108}=

$$2 \sqrt{ 75 } - \sqrt{ 12 } - \sqrt{ 108 } =$$

Evaluate

$$2\sqrt{3}\approx 3.464101615$$

Solution Steps

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}.

$$2\times 5\sqrt{3}-\sqrt{12}-\sqrt{108}$$

Multiply 2 and 5 to get 10.

$$10\sqrt{3}-\sqrt{12}-\sqrt{108}$$

Factor 12=2^{2}\times 3. Rewrite the square root of the product \sqrt{2^{2}\times 3} as the product of square roots \sqrt{2^{2}}\sqrt{3}. Take the square root of 2^{2}.

$$10\sqrt{3}-2\sqrt{3}-\sqrt{108}$$

Combine 10\sqrt{3} and -2\sqrt{3} to get 8\sqrt{3}.

$$8\sqrt{3}-\sqrt{108}$$

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}.

$$8\sqrt{3}-6\sqrt{3}$$

Combine 8\sqrt{3} and -6\sqrt{3} to get 2\sqrt{3}.

$$2\sqrt{3}$$