Solve 2sqrt{48}-sqrt{75}-sqrt{12}

$$2 \sqrt { 48 } - \sqrt { 75 } - \sqrt { 12 }$$

Evaluate

$$\sqrt{3}\approx 1.732050808$$

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}.

$$2\times 4\sqrt{3}-\sqrt{75}-\sqrt{12}$$

Multiply 2 and 4 to get 8.

$$8\sqrt{3}-\sqrt{75}-\sqrt{12}$$

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}.

$$8\sqrt{3}-5\sqrt{3}-\sqrt{12}$$

Combine 8\sqrt{3} and -5\sqrt{3} to get 3\sqrt{3}.

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

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}.

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

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

$$\sqrt{3}$$