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

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

Evaluate

$$5\sqrt{3}\approx 8.660254038$$

Solution Steps

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}.

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

Multiply -3 and 3 to get -9.

$$4\sqrt{3}-9\sqrt{3}+2\sqrt{75}$$

Combine 4\sqrt{3} and -9\sqrt{3} to get -5\sqrt{3}.

$$-5\sqrt{3}+2\sqrt{75}$$

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}.

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

Multiply 2 and 5 to get 10.

$$-5\sqrt{3}+10\sqrt{3}$$

Combine -5\sqrt{3} and 10\sqrt{3} to get 5\sqrt{3}.

$$5\sqrt{3}$$