Solve sqrt{108}+5sqrt{3}-sqrt{192}

$$\sqrt{ 108 } +5 \sqrt{ 3 } - \sqrt{ 192 }$$

Evaluate

$$3\sqrt{3}\approx 5.196152423$$

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}.

$$6\sqrt{3}+5\sqrt{3}-\sqrt{192}$$

Combine 6\sqrt{3} and 5\sqrt{3} to get 11\sqrt{3}.

$$11\sqrt{3}-\sqrt{192}$$

Factor 192=8^{2}\times 3. Rewrite the square root of the product \sqrt{8^{2}\times 3} as the product of square roots \sqrt{8^{2}}\sqrt{3}. Take the square root of 8^{2}.

$$11\sqrt{3}-8\sqrt{3}$$

Combine 11\sqrt{3} and -8\sqrt{3} to get 3\sqrt{3}.

$$3\sqrt{3}$$