Solve sqrt{108}+4sqrt{75}-3sqrt{27}-2sqrt{12}

$$\sqrt{ 108 } +4 \sqrt{ 75 } -3 \sqrt{ 27 } -2 \sqrt{ 12 }$$

Evaluate

$$13\sqrt{3}\approx 22.516660498$$

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}.

$$6\sqrt{3}+4\sqrt{75}-3\sqrt{27}-2\sqrt{12}$$

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}.

$$6\sqrt{3}+4\times 5\sqrt{3}-3\sqrt{27}-2\sqrt{12}$$

Multiply 4 and 5 to get 20.

$$6\sqrt{3}+20\sqrt{3}-3\sqrt{27}-2\sqrt{12}$$

Combine 6\sqrt{3} and 20\sqrt{3} to get 26\sqrt{3}.

$$26\sqrt{3}-3\sqrt{27}-2\sqrt{12}$$

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}.

$$26\sqrt{3}-3\times 3\sqrt{3}-2\sqrt{12}$$

Multiply -3 and 3 to get -9.

$$26\sqrt{3}-9\sqrt{3}-2\sqrt{12}$$

Combine 26\sqrt{3} and -9\sqrt{3} to get 17\sqrt{3}.

$$17\sqrt{3}-2\sqrt{12}$$

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}.

$$17\sqrt{3}-2\times 2\sqrt{3}$$

Multiply -2 and 2 to get -4.

$$17\sqrt{3}-4\sqrt{3}$$

Combine 17\sqrt{3} and -4\sqrt{3} to get 13\sqrt{3}.

$$13\sqrt{3}$$