Solve sqrt{75}+2sqrt{108}-3sqrt{3}=

$$\sqrt { 75 } + 2 \sqrt { 108 } - 3 \sqrt { 3 } =$$

Evaluate

$$14\sqrt{3}\approx 24.248711306$$

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}.

$$5\sqrt{3}+2\sqrt{108}-3\sqrt{3}$$

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}.

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

Multiply 2 and 6 to get 12.

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

Combine 5\sqrt{3} and 12\sqrt{3} to get 17\sqrt{3}.

$$17\sqrt{3}-3\sqrt{3}$$

Combine 17\sqrt{3} and -3\sqrt{3} to get 14\sqrt{3}.

$$14\sqrt{3}$$