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

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

Evaluate

$$-4\sqrt{3}\approx -6.92820323$$

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 -7\sqrt{3}.

$$-7\sqrt{3}+3\sqrt{3}$$

Combine -7\sqrt{3} and 3\sqrt{3} to get -4\sqrt{3}.

$$-4\sqrt{3}$$